{"id":27244,"date":"2021-09-25T13:00:57","date_gmt":"2021-09-25T13:00:57","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27244"},"modified":"2024-09-16T11:51:26","modified_gmt":"2024-09-16T11:51:26","slug":"%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%95%e0%a5%8d%e0%a4%b7%e0%a5%87%e0%a4%aa%e0%a5%8d%e0%a4%af-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%95%e0%a5%80-%e0%a4%97%e0%a4%a3%e0%a4%a8%e0%a4%be-%e0%a4%95%e0%a5%88","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%95%e0%a5%8d%e0%a4%b7%e0%a5%87%e0%a4%aa%e0%a5%8d%e0%a4%af-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%95%e0%a5%80-%e0%a4%97%e0%a4%a3%e0%a4%a8%e0%a4%be-%e0%a4%95%e0%a5%88\/","title":{"rendered":"\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f<\/h1>\n<p><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u0947 \u0938\u092d\u0940 \u0917\u0924\u093f\u0935\u093f\u091c\u094d\u091e\u093e\u0928 \u092a\u0939\u0932\u0941\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u092d\u094c\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f \u0939\u0948 \u091c\u094b \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0924\u094d\u0935\u0930\u093f\u0924 \u0917\u0924\u093f \u092a\u0930 \u0939\u092e\u093e\u0930\u0947 \u092a\u093f\u091b\u0932\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947, \u0917\u0924\u093f \u0915\u0940 \u0926\u093f\u0936\u093e \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927 \u0939\u091f\u093e\u0928\u0947 \u092a\u0930, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0947 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u092a\u0930\u0935\u0932\u092f\u093f\u0915 \u092a\u0925 \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u092e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0926\u093f\u0936\u093e \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f, \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0924\u094d\u0935\u0930\u0915 \u0915\u0947 \u0938\u093e\u0925 \u092e\u093f\u0932\u0915\u0930, \u0907\u0928 \u0917\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u0906\u0915\u093e\u0930 \u0926\u0947\u0924\u0940 \u0939\u0948\u0964<br \/>\n.<\/em><\/p>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><strong>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u0924\u0915, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0917\u093e:<\/p>\n<ol>\n<li><strong>\u0938\u094d\u092e\u0930\u0923<\/strong> \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u0940 \u092e\u094c\u0932\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0914\u0930 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u0913\u0902 \u0915\u094b (\u091c\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f, \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923, \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0924\u094d\u0935\u0930\u0915)\u0964<\/li>\n<li><strong>\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e<\/strong> \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0947 \u092a\u0925 \u0915\u094b \u0917\u094d\u0930\u093e\u092b\u093c\u093f\u0915 \u0930\u0942\u092a \u0938\u0947\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u093e\u0928\u093e<\/strong> \u0915\u0948\u0938\u0947 \u0917\u0924\u093f \u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u091a\u0930\u0923 (\u0906\u0930\u094b\u0939\u0923, \u091a\u0930\u092e \u092c\u093f\u0902\u0926\u0941, \u0905\u0935\u0930\u094b\u0939\u0923) \u0917\u0924\u093f\u0935\u093f\u091c\u094d\u091e\u093e\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<li><strong>\u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0930\u0928\u093e<\/strong> \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 \u091c\u093f\u0928\u092e\u0947\u0902 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908, \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0938\u0940\u092e\u093e \u0914\u0930 \u0915\u0941\u0932 \u0909\u0921\u093c\u093e\u0928 \u0938\u092e\u092f \u0915\u0940 \u0917\u0923\u0928\u093e \u0936\u093e\u092e\u093f\u0932 \u0939\u0948, \u092a\u0930\u0935\u0932\u092f\u093f\u0915 \u0917\u0924\u093f \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947\u0964<\/li>\n<li><strong>\u0935\u093f\u0918\u091f\u0928 \u0915\u0930\u0928\u093e<\/strong> \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u092f\u0939 \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0918\u091f\u0915 (\u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f, \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923, \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0924\u094d\u0935\u0930\u0915) \u0915\u0941\u0932 \u092a\u0925 \u0915\u094b \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n<p><center><\/p>\n<p><strong>\u0935\u093f\u0937\u092f \u0938\u0942\u091a\u0940<\/strong><br \/>\n<a href=\"#1\"><strong>\u092a\u0930\u093f\u091a\u092f<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u093e \u0935\u093f\u0915\u093e\u0938<\/strong><\/a><br \/>\n<a href=\"#3\">\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0940 \u0917\u0908 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u0915\u094b \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0947\u0902?<\/a><br \/>\n<a href=\"#4\">\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0947 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0947\u0902?<\/a><br \/>\n<a href=\"#5\">\u0915\u094c\u0928 \u0938\u093e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u0915\u0930\u0924\u093e \u0939\u0948?<\/a><br \/>\n<a href=\"#6\"><strong>\u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0905\u092d\u094d\u092f\u093e\u0938<\/strong><\/a>\n<\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/_dXgQ_7u5GE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u092a\u0930\u093f\u091a\u092f<\/h2>\n<p style=\"text-align: justify; color: #000000;\">\u092a\u093f\u091b\u0932\u0940 \u0915\u0915\u094d\u0937\u093e\u0913\u0902 \u092e\u0947\u0902 \u0939\u092e\u0928\u0947 <a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw\" rel=\"noopener\" target=\"_blank\">\u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0924\u094d\u0935\u0930\u093f\u0924 \u0930\u0947\u0916\u0940\u092f \u0917\u0924\u093f<\/a> \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u092f\u093e \u0914\u0930 \u0926\u0947\u0916\u093e \u0915\u093f \u091c\u092c \u090f\u0915 \u0938\u092e\u093e\u0928 \u0924\u094d\u0935\u0930\u0915 \u0915\u094b \u0917\u0924\u093f \u0915\u0940 \u0926\u093f\u0936\u093e \u092e\u0947\u0902 \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091c\u092c \u0939\u092e \u0926\u093f\u0936\u093e \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927 \u0939\u091f\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0924\u094d\u0935\u0930\u093f\u0924 \u0917\u0924\u093f \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0905\u092c \u092f\u0939 \u0930\u0947\u0916\u0940\u092f \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940\u0964 \u0907\u0938 \u092a\u0930\u093f\u0926\u0943\u0936\u094d\u092f \u092e\u0947\u0902, \u0917\u0924\u093f \u090f\u0915 \u092a\u0930\u0935\u0932\u092f\u093f\u0915 \u091a\u093e\u092a \u092a\u0930 \u0935\u093f\u0915\u0938\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0914\u0930 \u092f\u0939\u0940\u0902 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0936\u0941\u0930\u0942 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u092e\u0947\u0902, \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f \u0915\u093f\u0938\u0940 \u092d\u0940 \u0926\u093f\u0936\u093e \u092e\u0947\u0902 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u091c\u092c\u0915\u093f \u0924\u094d\u0935\u0930\u0915 \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0926\u093f\u0936\u093e \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u091c\u092c \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u093e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0938\u0940\u0927\u0947 \u090a\u092a\u0930 \u0915\u0940 \u0913\u0930 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0939\u092e\u0947\u0902 \u090f\u0915 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u094b \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0924\u094d\u0935\u0930\u093f\u0924 \u0917\u0924\u093f \u0915\u093e \u090f\u0915 \u092e\u093e\u092e\u0932\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u093e \u0935\u093f\u0915\u093e\u0938<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=172s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0939\u0948<\/span><\/strong><\/a> \u091c\u093f\u0938\u0947 \u091c\u092e\u0940\u0928 \u0938\u0947 \u090f\u0915 \u0924\u094b\u092a \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">v_0<\/span> \u0914\u0930 \u090f\u0915 \u091d\u0941\u0915\u093e\u0935 \u0915\u094b\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u0915\u0947 \u0938\u093e\u0925 \u0939\u0935\u093e \u092e\u0947\u0902 \u092a\u094d\u0930\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0940 \u0917\u0924\u093f \u0915\u094b \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0909\u0938\u0915\u0947 \u092a\u0925 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0926\u0940 \u0917\u0908 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u0915\u0930 \u092e\u0949\u0921\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092f\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\vec{a}(t) &amp; = (0,-g) \\\\ \\\\\n\n\\vec{v}(t) &amp; =\\displaystyle \\int (0,-g) dt = (v_{0x}, -gt+v_{0y})\\\\ \\\\\n\n\\vec{r}(t) &amp; =\\displaystyle \\int (v_{0x}, -gt+v_{0y}) dt = \\left(v_{0x}t + x_0, -\\frac{1}{2}gt^2+v_{0y}t + y_0\\right)\n\n\\end{array}<\/span>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-JQFKmGORl8A\/YVB9tKzayMI\/AAAAAAAAFks\/KPaXIUIcIVQ2yOAa_N9leIPgcZY6iv5zQCLcBGAsYHQ\/s0\/proyectil.PNG\" width=\"694\" height=\"390\" alt=\"\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u093e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-JQFKmGORl8A\/YVB9tKzayMI\/AAAAAAAAFks\/KPaXIUIcIVQ2yOAa_N9leIPgcZY6iv5zQCLcBGAsYHQ\/s0\/proyectil.PNG\" width=\"694\" height=\"390\" alt=\"\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u093e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v}_{0} = (v_{0x},v_{0y})<\/span> \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0935\u0947\u0917 \u0939\u0948, <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}_0=(x_0,y_0)<\/span> \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0939\u0948, \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">g=9.81[m\/s^2]<\/span> \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0915\u093e \u0924\u094d\u0935\u0930\u0915 \u0939\u0948\u0964 \u0905\u092c, \u092f\u0926\u093f \u0939\u092e \u092a\u093f\u091b\u0932\u0947 \u092a\u0948\u0930\u093e\u0917\u094d\u0930\u093e\u092b \u0915\u094b \u0926\u0947\u0916\u0947\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u092f\u0939 \u092a\u0924\u093e \u091a\u0932\u0947\u0917\u093e \u0915\u093f \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u093e \u0935\u0947\u0917 \u0938\u0940\u0927\u0947 \u0928\u0939\u0940\u0902 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u0907\u0938\u0915\u0940 \u0917\u0924\u093f \u0914\u0930 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923 \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902\u0964 \u0907\u0938 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0914\u0930 \u0925\u094b\u0921\u093c\u0940 \u0938\u0940 \u0924\u094d\u0930\u093f\u0915\u094b\u0923\u092e\u093f\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0935\u0947\u0917 \u0915\u094b \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nv_{0x} &amp;= v_0 \\cos(\\theta) \\\\\n\nv_{0y} &amp;= v_0 \\sin(\\theta)\n\n\\end{array}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">v_0 = \\|\\vec{v}_0\\|<\/span> \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0935\u0947\u0917 \u0915\u0940 \u092a\u0930\u093f\u092e\u093e\u0923 \u0939\u0948\u0964 \u092f\u0926\u093f \u0939\u092e \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0)=(0,0)<\/span> \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092a\u0925 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\vec{a}(t) &amp; = (0,-g) \\\\ \\\\\n\n\\vec{v}(t) &amp; =(v_{0}\\cos(\\theta), -gt+v_{0}\\sin(\\theta)\\\\ \\\\\n\n\\vec{r}(t) &amp; \\displaystyle =\\left(v_{0}\\cos(\\theta)t , -\\frac{1}{2}gt^2+v_{0}\\sin(\\theta)t \\right)\n\n\\end{array}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938\u0915\u0947 \u0938\u093e\u0925 \u0939\u092e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0915\u0941\u091b \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u093e \u0909\u0924\u094d\u0924\u0930 \u0926\u0947 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902: \u092f\u0939 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930 \u091c\u093e\u090f\u0917\u093e? \u092f\u0939 \u0915\u093f\u0924\u0928\u0940 \u090a\u0902\u091a\u093e\u0908 \u0924\u0915 \u092a\u0939\u0941\u0902\u091a\u0947\u0917\u093e? \u0917\u093f\u0930\u0928\u0947 \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u0938\u092e\u092f \u0932\u0917\u0947\u0917\u093e? \u0906\u0926\u093f\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0940 \u0917\u0908 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u0915\u094b \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0947\u0902?<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=398s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u093e \u0909\u0924\u094d\u0924\u0930 \u0926\u0947\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f<\/span><\/strong><\/a> \u0939\u092e\u0947\u0902 \u0916\u0941\u0926 \u0938\u0947 \u092a\u0942\u091b\u0928\u093e \u0939\u094b\u0917\u093e: \u091c\u092c \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0905\u092a\u0928\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u092a\u0939\u0941\u0902\u091a\u0924\u093e \u0939\u0948 \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? \u091c\u094b \u0939\u094b\u0924\u093e \u0939\u0948 \u0935\u0939 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0907\u0938\u0915\u0947 \u0935\u0947\u0917 \u0915\u093e \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0918\u091f\u0915 \u0936\u0942\u0928\u094d\u092f \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0932\u093f\u090f:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> -gt+v_{0}\\sin(\\theta) = 0 <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u092f\u0939 \u0915\u0939\u0928\u0947 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> t = \\displaystyle \\frac{v_{0}\\sin(\\theta)}{g} <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0905\u0930\u094d\u0925\u093e\u0924, \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u092a\u0939\u0941\u0902\u091a\u0924\u093e \u0939\u0948 \u091c\u092c \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u0947 \u092c\u093e\u0926 <span class=\"katex-eq\" data-katex-display=\"false\">t=v_0\\sin(\\theta)\/g<\/span> \u0915\u093e \u0938\u092e\u092f \u0917\u0941\u091c\u0930 \u091a\u0941\u0915\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0939\u092e \u0907\u0938\u0947 \u00ab\u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u0915\u093e \u0938\u092e\u092f\u00bb \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0932\u093f\u0916\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{t_{alt.max} = \\frac{v_{0}\\sin(\\theta)}{g}}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u092b\u093f\u0930, \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0928\u0947 \u0935\u093e\u0932\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u0915\u094b \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0918\u091f\u0915 \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">t=t_{alt.max}<\/span> \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\ny_{alt.max} &amp; = \\displaystyle -\\frac{1}{2}gt_{alt.max}^2+v_{0}\\sin(\\theta)t_{alt.max}\\\\ \\\\\n\n&amp; =\\displaystyle-\\frac{1}{2}g \\left(\\frac{v_{0}\\sin(\\theta)}{g} \\right)^2 + v_{0}\\sin(\\theta) \\frac{v_{0}\\sin(\\theta)}{g} \\\\ \\\\\n\n&amp; =\\displaystyle-\\frac{1}{2} \\frac{v_{0}^2\\sin^2(\\theta)}{g} + \\frac{v_{0}^2\\sin^2(\\theta)}{g} \\\\ \\\\\n\n&amp; =\\displaystyle \\frac{v_{0}^2\\sin^2(\\theta)}{2g}\n\n\\end{array}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0947 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0947\u0902?<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=653s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u092f\u0926\u093f \u0906\u092a \u092f\u0939 \u091c\u093e\u0928\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f<\/span><\/strong><\/a> \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u091c\u092e\u0940\u0928 \u0915\u094b \u091b\u0942\u0928\u0947 \u0924\u0915 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0924\u092f \u0915\u0930\u0924\u093e \u0939\u0948, \u0924\u094b \u0906\u092a\u0915\u094b \u092c\u0938 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0938\u0947 \u092a\u0942\u091b\u0928\u093e \u0939\u0948\u0964 \u0932\u0947\u0915\u093f\u0928 \u0939\u092e \u0910\u0938\u093e \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902? \u0938\u0930\u0932: \u091c\u092c \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u091c\u092e\u0940\u0928 \u0915\u094b \u091b\u0942\u0924\u093e \u0939\u0948 \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? \u091c\u094b \u0939\u094b\u0924\u093e \u0939\u0948 \u0935\u0939 \u092f\u0939 \u0939\u0948 \u0915\u093f \u090a\u0902\u091a\u093e\u0908 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0936\u0942\u0928\u094d\u092f \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle -\\frac{1}{2}gt^2+v_{0}\\sin(\\theta)t = 0\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u092f\u0939\u093e\u0902 \u0939\u092e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0947 \u091c\u092e\u0940\u0928 \u0915\u094b \u091b\u0942\u0928\u0947 \u0915\u0947 \u0938\u092e\u092f \u0915\u094b \u0939\u0932 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0926\u094b \u092c\u093e\u0930 \u0939\u094b\u0924\u093e \u0939\u0948: \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u0947 \u0938\u092e\u092f \u0914\u0930 \u091c\u092c \u092f\u0939 \u0917\u093f\u0930\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u092e\u093e\u0927\u093e\u0928 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nt &amp; = 0\\\\ \\\\\n\nt &amp; = \\displaystyle \\frac{2v_0 \\sin(\\theta)}{g}\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0917\u0948\u0930-\u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u0939\u092e \u00ab\u0917\u093f\u0930\u093e\u0935\u091f \u0915\u093e \u0938\u092e\u092f\u00bb \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0932\u093f\u0916\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{t_{caida} = \\displaystyle \\frac{2v_0 \\sin(\\theta)}{g}}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u092f\u0926\u093f \u0906\u092a \u090a\u092a\u0930 \u0926\u0947\u0916\u0947\u0902, \u0924\u094b \u0906\u092a\u0915\u094b \u092f\u0939 \u092a\u0924\u093e \u091a\u0932\u0947\u0917\u093e \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">t_{caida} = 2t_{alt.max}<\/span> \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u094b \u0905\u092a\u0928\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u0924\u0915 \u092a\u0939\u0941\u0902\u091a\u0928\u0947 \u092e\u0947\u0902 \u091c\u093f\u0924\u0928\u093e \u0938\u092e\u092f \u0932\u0917\u0924\u093e \u0939\u0948, \u0909\u0924\u0928\u093e \u0939\u0940 \u0938\u092e\u092f \u0907\u0938\u0947 \u0905\u092a\u0928\u0947 \u0909\u091a\u094d\u091a\u0924\u092e \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0917\u093f\u0930\u0928\u0947 \u092e\u0947\u0902 \u0932\u0917\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0940 \u0917\u0924\u093f \u092e\u0947\u0902 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0915\u093e \u0938\u0902\u0915\u0947\u0924 \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902, \u092f\u0939 \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u091c\u092c \u0906\u092a \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u090a\u0902\u091a\u093e\u0908 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u090f\u0915 \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0906\u0915\u093e\u0930 \u0932\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0917\u093f\u0930\u093e\u0935\u091f \u0915\u093e \u0938\u092e\u092f \u091c\u093e\u0928\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926, \u0905\u092c \u092f\u0939 \u0938\u0902\u092d\u0935 \u0939\u0948 \u0915\u093f \u091c\u092c \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u091c\u092e\u0940\u0928 \u0915\u094b \u091b\u0942\u0924\u093e \u0939\u0948 \u0924\u094b \u0909\u0938\u0928\u0947 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0924\u092f \u0915\u0940 \u0939\u0948, \u0907\u0938\u0947 \u092a\u0939\u0932\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0915\u0947 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nx_{caida} &amp;= v_{0}\\cos(\\theta)t_{caida} \\\\ \\\\\n\n&amp; = \\displaystyle v_{0}\\cos(\\theta)\\frac{2v_0 \\sin(\\theta)}{g} \\\\ \\\\\n\n&amp; = \\displaystyle \\frac{v_0^2 \\sin(2\\theta)}{g} \\\\ \\\\\n\n\\end{array}<\/span>\n<p><a name=\"5\"><\/a><\/p>\n<h3>\u0915\u094c\u0928 \u0938\u093e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u0915\u0930\u0924\u093e \u0939\u0948?<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_dXgQ_7u5GE&amp;t=999s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u092f\u0926\u093f \u0906\u092a \u092f\u0939 \u091c\u093e\u0928\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f<\/span><\/strong><\/a> \u0915\u094c\u0928 \u0938\u093e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u0915\u0930\u0924\u093e \u0939\u0948, \u092f\u093e \u0906\u092a \u092f\u0939 \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u091c\u094b \u0906\u092a \u091c\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u0935\u0939 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0938\u0939\u0940 \u0939\u0948, \u0924\u094b \u0906\u092a\u0915\u094b \u092c\u0938 \u0939\u092e\u093e\u0930\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0935\u0939 \u0932\u0947\u0928\u093e \u0939\u0948 \u091c\u094b \u0906\u092a\u0915\u094b \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u094b \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u0939\u092e\u0928\u0947 \u092a\u0939\u0932\u0947 \u0939\u0940 \u092a\u093f\u091b\u0932\u0947 \u0916\u0902\u0921 \u092e\u0947\u0902 \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930 \u0932\u0940 \u0939\u0948, \u0914\u0930 \u092f\u0939 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923 \u0915\u093e \u090f\u0915 \u0915\u093e\u0930\u094d\u092f \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle x_{caida} = x_{caida}(\\theta) = \\frac{v_0^2 \\sin(2\\theta)}{g}\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0938\u093e\u0907\u0928 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0947 \u0926\u094b \u091a\u0930\u092e \u092a\u0930\u093f\u0923\u093e\u092e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902: +1 \u0914\u0930 -1, \u0932\u0947\u0915\u093f\u0928 \u0939\u092e\u0947\u0902 \u092a\u0939\u0932\u0947 \u0935\u093e\u0932\u0947 \u092e\u0947\u0902 \u0930\u0941\u091a\u093f \u0939\u0948\u0964 <span class=\"katex-eq\" data-katex-display=\"false\">\\sin(2\\theta)=+1<\/span> \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">2\\theta = 90^o<\/span> (+<span class=\"katex-eq\" data-katex-display=\"false\">2k\\pi,<\/span> \u0932\u0947\u0915\u093f\u0928 \u0939\u092e \u0909\u0938 \u0939\u093f\u0938\u094d\u0938\u0947 \u0915\u094b \u091b\u094b\u0921\u093c \u0926\u0947\u0902\u0917\u0947 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0939\u092e\u0947\u0902 \u0907\u0938\u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u0948) \u0914\u0930 \u0907\u0938\u0932\u093f\u090f <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=45^o<\/span> \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u0923 \u0915\u094b\u0923 \u0939\u0948 \u091c\u094b \u0938\u0940\u092e\u093e \u0915\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u093e \u092d\u0940 \u0938\u0902\u092d\u0935 \u0939\u0948 \u092f\u0926\u093f \u0939\u092e \u0907\u0938\u0947 \u090f\u0915 \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0947\u0902 (\u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 <a href=\"https:\/\/www.youtube.com\/watch?v=OscTlX3raaE&#038;list=PL_C8rbeFjqAVaR_sgLJRBvMm5t6E1GxGI\" target=\"_blank\" rel=\"noopener\">\u0907\u0938 \u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0909\u092a\u0915\u0930\u0923<\/a>) \u0932\u0947\u0915\u093f\u0928 \u092e\u0948\u0902\u0928\u0947 \u0907\u0938 \u0930\u093e\u0938\u094d\u0924\u0947 \u0915\u094b \u091a\u0941\u0928\u093e \u0939\u0948 \u091c\u094b \u0924\u0947\u091c \u0939\u0948 \u0914\u0930 \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u091a\u093f\u0924\u094d\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948\u0964<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0905\u092d\u094d\u092f\u093e\u0938<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u090f\u0915 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u094b \u091c\u092e\u0940\u0928 \u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=30^o<\/span> \u0915\u0947 \u090a\u0902\u091a\u093e\u0908 \u0915\u094b\u0923 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">v_0=70[km\/h].<\/span> \u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f \u0915\u0947 \u0938\u093e\u0925 \u092a\u094d\u0930\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 a) \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0940 \u0917\u0908 \u0905\u0927\u093f\u0915\u0924\u092e \u090a\u0902\u091a\u093e\u0908 \u0915\u094d\u092f\u093e \u0939\u0948? b) \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0928\u0947 \u091c\u092e\u0940\u0928 \u0915\u094b \u091b\u0942\u0928\u0947 \u0924\u0915 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0924\u092f \u0915\u0940? c) \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u094b \u0917\u093f\u0930\u0928\u0947 \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u0938\u092e\u092f \u0932\u0917\u0924\u093e \u0939\u0948?<\/li>\n<li>\u090f\u0915 \u0924\u094b\u092a \u091c\u094b \u091c\u092e\u0940\u0928 \u092a\u0930 \u0930\u0916\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, 90[km\/h] \u0915\u0940 \u0917\u0924\u093f \u0938\u0947 \u090f\u0915 \u0917\u094b\u0932\u0940 \u0926\u093e\u0917\u0924\u0940 \u0939\u0948\u0964 \u0924\u094b\u092a \u0915\u094b \u0915\u093f\u0938 \u090a\u0902\u091a\u093e\u0908 \u0915\u094b\u0923 \u092a\u0930 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0924\u093e\u0915\u093f \u0917\u094b\u0932\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0926\u0942\u0930\u0940 20[m] \u092a\u0930 \u0917\u093f\u0930\u0947?<\/li>\n<li>\u092a\u093f\u091b\u0932\u0947 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0940 \u0935\u0939\u0940 \u0924\u094b\u092a \u0905\u092c 5[m] \u0915\u0940 \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u0930\u0916\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0947 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0938 \u090a\u0902\u091a\u093e\u0908 \u0915\u094b\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0924\u093e\u0915\u093f \u0917\u094b\u0932\u0940 \u0905\u092d\u0940 \u092d\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0926\u0942\u0930\u0940 20[m] \u092a\u0930 \u0917\u093f\u0930\u0947?<\/li>\n<li>\u090f\u0915 \u092c\u092e\u0935\u0930\u094d\u0937\u0915 3,000[m] \u0915\u0940 \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 1,500[km\/h] \u0915\u0940 \u0917\u0924\u093f \u0938\u0947 \u0909\u0921\u093c\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u092f\u0939 \u090f\u0915 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u094b \u0905\u092a\u0928\u0947 \u092d\u093e\u0930 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0917\u093f\u0930\u0928\u0947 \u0926\u0947\u0924\u093e \u0939\u0948, \u0924\u094b \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u091c\u092e\u0940\u0928 \u0915\u094b \u091b\u0942\u0928\u0947 \u0924\u0915 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0924\u092f \u0915\u0930\u0947\u0917\u093e?<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u0947 \u0938\u092d\u0940 \u0917\u0924\u093f\u0935\u093f\u091c\u094d\u091e\u093e\u0928 \u092a\u0939\u0932\u0941\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u092d\u094c\u0924\u093f\u0915\u0940 \u092e\u0947\u0902 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f \u0939\u0948 \u091c\u094b \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0924\u094d\u0935\u0930\u093f\u0924 \u0917\u0924\u093f \u092a\u0930 \u0939\u092e\u093e\u0930\u0947 \u092a\u093f\u091b\u0932\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947, \u0917\u0924\u093f \u0915\u0940 \u0926\u093f\u0936\u093e \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927 \u0939\u091f\u093e\u0928\u0947 \u092a\u0930, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0915\u0947 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u092a\u0930\u0935\u0932\u092f\u093f\u0915 \u092a\u0925 \u092e\u093f\u0932\u0924\u0947 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26193,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[643,659],"tags":[],"class_list":["post-27244","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-643","category-659"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u092a\u0930\u0935\u0932\u092f\u093f\u0915 \u092a\u0925 \u0914\u0930 \u0909\u0928\u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902, \u0914\u0930 \u0915\u0948\u0938\u0947 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