{"id":10609,"date":"2022-03-10T11:08:36","date_gmt":"2022-03-10T11:08:36","guid":{"rendered":"https:\/\/10minuteschool.com\/content\/?p=10609"},"modified":"2022-03-10T11:22:28","modified_gmt":"2022-03-10T11:22:28","slug":"projection-speed","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/projection-speed\/","title":{"rendered":"\u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa\u09a3 \u0997\u09a4\u09bf (Projection Speed)"},"content":{"rendered":"

\u09a4\u09c1\u09ae\u09bf \u09af\u09a6\u09bf \u09b8\u09cd\u099f\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09ae\u09c7 \u0995\u0996\u09a8\u0993 \u0995\u09cd\u09b0\u09bf\u0995\u09c7\u099f \u0996\u09c7\u09b2\u09be \u09a6\u09c7\u0996\u09a4\u09c7 \u09af\u09be\u0993 \u09a4\u09be\u09b9\u09b2\u09c7 \u09ac\u09be\u0989\u09a8\u09cd\u09a1\u09be\u09b0\u09bf \u09a5\u09c7\u0995\u09c7 \u099b\u09cb\u0981\u09a1\u09bc\u09be \u0995\u09cd\u09b0\u09bf\u0995\u09c7\u099f \u09ac\u09b2\u09c7\u09b0 \u0997\u09a4\u09bf<\/span> \u09b2\u0995\u09cd\u09b7 <\/span>\u0995\u09b0\u09b2\u09c7 \u09a6\u09c7\u0996\u09ac\u09c7 \u09ac\u09b2\u099f\u09bf \u09aa\u09cd\u09b0\u09a5\u09ae\u09c7 \u09ad\u09c2\u09ae\u09bf \u09a5\u09c7\u0995\u09c7 \u0989\u09aa\u09b0\u09c7 \u0993\u09a0\u09c7 \u09aa\u09c1\u09a8\u09b0\u09be\u09af\u09bc \u09ac\u09be\u0981\u0995\u09be \u09aa\u09a5\u09c7 \u09ad\u09c2\u09ae\u09bf\u09a4\u09c7 \u09ab\u09bf\u09b0\u09c7 \u0986\u09b8\u09c7\u0964 \u0986\u09ac\u09be\u09b0 \u09ac\u09a8\u09cd\u09a6\u09c1\u0995 \u09a5\u09c7\u0995\u09c7<\/span> \u0989\u09aa\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u099b\u09cb\u09a1\u09bc\u09be \u09ac\u09c1\u09b2\u09c7\u099f\u09c7\u09b0 \u0997\u09a4\u09bf<\/span>,<\/span> \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09a4\u09c0\u09b0 \u09ac\u09be \u09ac\u09b0\u09cd\u09b6\u09be\u09b0 \u0997\u09a4\u09bf<\/span>, <\/span>\u09ac\u09bf\u09ae\u09be\u09a8 \u09a5\u09c7\u0995\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 <\/span>\u09ac\u09cb\u09ae\u09be\u09b0 <\/span>\u0997\u09a4\u09bf \u09b8\u0995\u09b2 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7<\/span> \u098f\u0995<\/span>\u0987 \u09aa\u09cd\u09b0\u0995\u09be\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5 \u09b2\u0995\u09cd\u09b7 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u098f\u0987 \u09a7\u09b0\u09a8\u09c7\u09b0 \u09ac\u0995\u09cd\u09f0\u0997\u09a4\u09bf\u0995\u09c7 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf (Projection Speed )\u09ac\u09b2\u09c7 \u098f\u09ac\u0982 \u0997\u09a4\u09bf\u09aa\u09a5\u0995\u09c7 \u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa\u09a3 (<\/span>trajectory)<\/span> \u09ac\u09b2\u09c7\u0964 <\/span><\/p>\n

\u0987\u09b9\u09be \u098f\u0995\u099f\u09bf \u0985\u09a7\u09bf\u09ac\u09c3\u09a4\u09cd\u09a4<\/a><\/span>\u0964 <\/span>\u098f \u09a7\u09b0\u09a8\u09c7\u09b0 \u0997\u09a4\u09bf \u09a6\u09cd\u09ac\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u0997\u09a4\u09bf\u0964<\/span> \u09ac\u09be\u09a4\u09be\u09b8\u09c7\u09b0 \u09ac\u09be\u09a7\u09be \u0989\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u0995\u09b0\u09b2\u09c7 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf \u0995\u09c7\u09ac\u09b2\u09ae\u09be\u09a4\u09cd\u09b0 \u0985\u09ad\u09bf<\/span>\u0995\u09b0\u09cd\u09b7\u09c7\u09b0<\/span> \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09af\u09bc \u09b9\u09af\u09bc\u0964 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5 \u09b8\u09b0\u09cd\u09ac\u09a6\u09be \u09aa\u09cd\u09af\u09be\u09b0\u09be\u09ac\u09cb\u09b2\u09be \u09ac\u09be \u0985\u09a7\u09bf\u09ac\u09c3\u09a4\u09cd\u09a4 \u09b9\u09af\u09bc\u0964 \u09aa\u09cd\u09b0\u09be\u09b8 \u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u0989\u099a\u09cd\u099a\u09a4\u09be\u09af\u09bc \u09aa\u09cc\u099b\u09be\u09b2\u09c7 \u098f\u09b0 \u09ac\u09c7\u0997 \u09b8\u09b0\u09cd\u09ac\u09a8\u09bf\u09ae\u09cd\u09a8 \u09b9\u09af\u09bc\u0964 \u0986\u09ac\u09be\u09b0 \u09b8\u09b0\u09cd\u09ac\u09be\u09a7\u09bf\u0995 \u0989\u099a\u09cd\u099a\u09a4\u09be\u09af\u09bc \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf \u098f\u0995\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u09b9\u09af\u09bc\u0964<\/span> \u09aa\u09cd\u09b0\u09be\u09b8 \u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa\u09a3 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09a6\u09bf\u0995\u09c7 \u09b8\u09b0\u09cd\u09ac\u09be\u09a7\u09bf\u0995 \u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span> \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 \u09a4\u09be\u0995\u09c7 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u09aa\u09be\u09b2\u09cd\u09b2\u09be (<\/span>Range)<\/span> \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\"Projection<\/p>\n

\u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u09a4\u09cd\u09ac\u09b0\u09a3<\/span> a<\/span>x<\/span>=0,\u00a0<\/span>\u0989\u09b2\u09cd\u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u09a4\u09cd\u09ac\u09b0\u09a3<\/span>, <\/span>a<\/span>y<\/span>=-g\u00a0 <\/span>\u09b9\u09af\u09bc\u0964 \u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa\u09a3 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09aa\u09cd\u09f0\u09be\u09b8\u09c7\u09b0 \u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0982\u0995<\/span> x=0,\u00a0 y=0<\/span> \u09b9\u09af\u09bc\u0964 \u09ae\u09a8\u09c7 \u0995\u09b0 <\/span>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 <\/span> \u0995\u09cb\u09a3\u09c7 \u098f\u0995\u099f\u09bf \u09aa\u09cd\u09b0\u09be\u09b8\u0995\u09c7 <\/span>v<\/span>0<\/span> \u0986\u09a6\u09bf\u09ac\u09c7\u0997\u09c7 \u0989\u09aa\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09c7\u09aa<\/span> \u09b9\u09b2\u09cb [\u099a\u09bf\u09a4\u09cd\u09b0]<\/span>\u0964 <\/span>\u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a5\u09ae\u09bf\u0995 \u09ac\u09c7\u0997 <\/span>v<\/span>0<\/span> \u0995\u09c7 \u09a6\u09c1\u099f\u09bf \u0989\u09aa\u09be\u0982\u09b6\u09c7 \u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u098f\u0995\u099f\u09bf \u0989\u09aa\u09be\u0982\u09b6 <\/span>OX<\/span>\u00a0 <\/span>\u09ac\u09b0\u09be\u09ac\u09b0<\/span>, <\/span>\u0989\u09aa\u09be\u0982\u09b6 <\/span>OY<\/span> \u09ac\u09b0\u09be\u09ac\u09b0\u0964 \u0989\u09aa\u09be\u0982\u09b6 \u09a6\u09c1\u099f\u09bf \u09b9\u09b2\u09cb <\/span>v<\/span>x<\/span>0<\/span>=<\/span>v<\/span>0<\/span>cos<\/span> \u098f\u09ac\u0982 <\/span>v<\/span>y<\/span>0<\/span>=<\/span>v<\/span>0<\/span>sin<\/span> \u0964<\/span><\/p>\n

\u0986\u09ae\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa \u09ae\u09c1\u09b9\u09c2\u09b0\u09cd\u09a4 \u09a5\u09c7\u0995\u09c7 \u09b8\u09ae\u09af\u09bc \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09bf\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>t=0<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span> x<\/span> \u09b9\u09b2\u09c7<\/span>,<\/span><\/p>\n

x=<\/span>v<\/span>x<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>a<\/span>x<\/span>t<\/span>2<\/span><\/p>\n

x=<\/span>v<\/span>0<\/span>cos<\/span> \u03b8t<\/span> +0<\/span> [\u2235<\/span> \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u0997\u09a4\u09bf <\/span>v<\/span>x<\/span>0<\/span>=<\/span>v<\/span>0<\/span>cos<\/span> \u00a0]<\/span><\/p>\n

\u2234t=<\/span>x<\/span>v<\/span>0<\/span>cos<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0 <\/span>a<\/span>x<\/span>=-g\u00a0<\/span>\u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc \u09aa\u09b0 \u0989\u09b2\u09cd\u09b2\u09ae\u09cd\u09ac \u09a6\u09bf\u0995\u09c7 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u09ac\u09c7\u0997 \u09ac\u09be \u0989\u09b2\u09cd\u09b2\u09ae\u09cd\u09ac \u0997\u09a4\u09bf<\/span><\/p>\n

v<\/span>y<\/span>=<\/span>v<\/span>y<\/span>0<\/span>-gt=<\/span>v<\/span>0<\/span>sin<\/span> -gt<\/span><\/p>\n

t\u00a0<\/span>\u09b8\u09ae\u09af\u09bc \u09aa\u09b0 \u09aa\u09cd\u09b0\u09be\u09b8 \u09af\u09a6\u09bf <\/span>y<\/span> \u0989\u099a\u09cd\u099a\u09a4\u09be\u09af\u09bc<\/span> \u0986\u09b0\u09cb\u09b9\u09a3 <\/span>\u0995\u09b0\u09c7<\/span>, \u09a4\u09ac\u09c7\u00a0<\/span><\/p>\n

y=<\/span>v<\/span>y0<\/span>t-<\/span>1<\/span>2<\/span>g<\/span>t<\/span>2<\/span>=<\/span>v<\/span>0<\/span>sin<\/span> \u03b8t<\/span> –<\/span>1<\/span>2<\/span>g<\/span>t<\/span>2<\/span><\/p>\n

t<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u09b2\u09a6\u09cd\u09a7\u09bf \u09ac\u09c7\u0997<\/span>,<\/span> v=<\/span>v<\/span>x<\/span>2<\/span>+<\/span>v<\/span>y<\/span>2<\/span><\/p>\n

\u09b2\u09a6\u09cd\u09a7\u09bf \u09ac\u09c7\u0997 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09a6\u09bf\u0995\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 <\/span> \u0995\u09cb\u09a3 \u0995\u09b0\u09b2\u09c7<\/span>, <\/span>tan<\/span> =<\/span>v<\/span>y<\/span>v<\/span>x<\/span><\/p>\n

t<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 <\/span>(<\/span>3.14)\u00a0<\/span>\u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n

y=<\/span>v<\/span>0<\/span>sin<\/span> x<\/span>v<\/span>0<\/span>cos<\/span> –<\/span>1<\/span>2<\/span>g\u00d7<\/span>x<\/span>2<\/span>v<\/span>0<\/span>2<\/span><\/p>\n

y=<\/span>tan<\/span> x-<\/span>8<\/span>2<\/span>v<\/span>0<\/span>2<\/span> x<\/span>2<\/span><\/p>\n

y=ax-b<\/span>x<\/span>2<\/span> \u2026 \u2026 <\/span>\u0987\u09b9\u09be \u098f\u0995\u099f\u09bf \u09aa\u09cd\u09af\u09be\u09b0\u09be<\/span>\u09ac\u09cb<\/span>\u09b2\u09be \u09ac\u09be \u0985\u09a7\u09bf\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0<\/span>\u0995\u09b0\u09a3\u0964\u00a0<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7, <\/span>a=<\/span>tan<\/span> ,b=<\/span>g<\/span>2<\/span>v<\/span>0<\/span>2<\/span><\/p>\n

\u098f\u0987 \u09b0\u09be\u09b6\u09bf \u09a6\u09c1\u099f\u09bf \u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa \u09aa\u09a5\u09c7 \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5 \u098f\u0995\u099f\u09bf\u00a0 \u09aa\u09cd\u09af\u09be\u09b0\u09be\u09ac\u09cb\u09b2\u09be\u0964<\/span><\/p>\n

\u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa\u09a3 \u0997\u09a4\u09bf\u00a0 \u09ac\u09bf\u09b7\u09df\u0995 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09b0\u09be\u09b6\u09bf (Projection Speed Related Terms)<\/h2>\n

\u09b8\u09b0\u09cd\u09ac\u09be\u09a7\u09bf\u0995 \u0989\u099a\u09cd\u099a\u09a4\u09be <\/b>(<\/b>H<\/span>): <\/b>\u00a0<\/span>\u09b8\u09b0\u09cd\u09ac\u09cb\u099a\u09cd\u099a \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>A<\/span>–<\/span>\u09a4\u09c7 \u09ac\u09c7\u0997\u09c7\u09b0 \u0989\u09b2\u09cd\u09b2\u09ae\u09cd\u09ac\u00a0 \u0989\u09aa\u09be\u0982\u09b6\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09af\u09bc \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>v<\/span>y<\/span>=0<\/span> \u09b9\u09af\u09bc<\/span><\/p>\n

\u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 <\/span>v<\/span>0<\/span>sin<\/span> -gt=0,t=<\/span>v<\/span>0<\/span>sin<\/span> g<\/span>\u00a0<\/span><\/p>\n

\u00a0\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 <\/span>y=H<\/span> \u098f\u09ac\u0982<\/span> t<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc,\u00a0<\/span><\/p>\n

H=<\/span>v<\/span>0<\/span>sin<\/span> v<\/span>0<\/span>sin<\/span> 8<\/span>–<\/span>1<\/span>2<\/span>g<\/span>v<\/span>0<\/span>2<\/span> g<\/span>2<\/span><\/p>\n

H=<\/span>v<\/span>0<\/span>2<\/span> g<\/span>–<\/span>v<\/span>0<\/span>2<\/span> 2g<\/span><\/p>\n

=<\/span>v<\/span>0<\/span>2<\/span> 8<\/span>1-<\/span>1<\/span>2<\/span>=<\/span>v<\/span>0<\/span>2<\/span> 2g<\/span><\/p>\n

\u2234H=<\/span>v<\/span>0<\/span>2<\/span> 2g<\/span><\/p>\n

\u09ac\u09bf\u099a\u09b0\u09a3 \u0995\u09be\u09b2 <\/b>(T): <\/b>\u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0989\u09a0\u09be \u098f\u09ac\u0982 \u09a8\u09be\u09ae\u09be\u09b0 \u099c\u09a8\u09cd\u09af <\/span>y=0<\/span> \u09b9\u09af\u09bc<\/span><\/p>\n

\u09ab\u09b2\u09c7 <\/span>(2<\/span>)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 <\/span>v<\/span>0<\/span>sin<\/span> \u03b8t<\/span> –<\/span>1<\/span>2<\/span>g<\/span>t<\/span>2<\/span>=0<\/span><\/p>\n

\u2234t<\/span>v<\/span>0<\/span>sin<\/span> –<\/span>1<\/span>2<\/span>gt<\/span>=0<\/span><\/p>\n

\u2234\u2206t=<\/span>2<\/span>v<\/span>0<\/span>sin<\/span> 8<\/span><\/p>\n

t=0<\/span>\u00a0<\/span>\u09b9\u09b2\u09c7<\/span>\u00a0<\/span>\u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0<\/span>\u00a0<\/span>\u09aa\u09cd\u09b0\u09be\u09a5\u09ae\u09bf\u0995<\/span>\u00a0<\/span>\u0985\u09ac\u09b8\u09cd\u09a5\u09be<\/span>\u00a0<\/span>0<\/span>-\u0995\u09c7<\/span>\u00a0<\/span>\u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6<\/span>\u00a0<\/span>\u0995\u09b0\u09c7\u0964<\/span>\u00a0<\/span>\u0985\u09a4\u098f\u09ac<\/span>\u00a0<\/span>\u09ac\u09bf\u099a\u09b0\u09a3<\/span>\u00a0<\/span>\u0995\u09be\u09b2<\/span>\u00a0t\u00a0=\u00a0<\/span>T<\/span>\u00a0<\/span>\u09ac\u09b8\u09bf\u09af\u09bc\u09c7<\/span>\u00a0<\/span>\u09aa\u09be\u0987<\/span><\/p>\n

T=<\/span>2<\/span>v<\/span>0<\/span>sin<\/span> 8<\/span><\/p>\n

\u09aa\u09cd\u09b0\u0995\u09cd\u09b7\u09c7\u09aa\u09a3 \u09b8\u09c0\u09ae\u09be \u09ac\u09be \u09aa\u09be\u09b2\u09cd\u09b2\u09be <\/b>(R) : <\/b>\u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09a6\u09bf\u0995\u09c7 <\/span>OB<\/span> = <\/span>\u09aa\u09be\u09b2\u09cd\u09b2\u09be <\/span>= <\/span>R<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac \u09aa\u09be\u09b2\u09cd\u09b2\u09be<\/span>, <\/span>R=<\/span>v<\/span>x<\/span>0<\/span>T=<\/span>v<\/span>0<\/span>cos<\/span> T<\/span> =<\/span>v<\/span>0<\/span>cos<\/span> 2<\/span>v<\/span>0<\/span>sin<\/span> g<\/span>=<\/span>2<\/span>v<\/span>0<\/span>2<\/span>sin<\/span> cos<\/span> \u00a0 <\/span>8<\/span><\/p>\n

R=<\/span>v<\/span>0<\/span>2<\/span>8<\/span>s<\/span><\/p>\n

\u09b8\u09b0\u09cd\u09ac\u09be\u09a7\u09bf\u0995 \u09aa\u09be\u09b2\u09cd\u09b2\u09be<\/b> (<\/b>R<\/span>max<\/span>):<\/b> v<\/span>0<\/span> \u098f\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09ae\u09be\u09a8\u09c7 <\/span>R <\/span>\u09b8\u09b0\u09cd\u09ac\u09be\u09a7\u09bf\u0995 \u09b9\u09af\u09bc \u09af\u0996\u09a8 <\/span>sin<\/span> 2\u03b8<\/span> =1<\/span> \u09ac\u09be <\/span>2\u03b8=<\/span>90<\/span> \u09b9\u09af\u09bc \u09ac\u09be <\/span>\u03b8=<\/span>45<\/span> \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

R<\/span>max<\/span>=<\/span>v<\/span>0<\/span>2<\/span>sin<\/span> 90<\/span> g<\/span>=<\/span>v<\/span>0<\/span>2<\/span>g<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>45<\/span> \u09a8\u09bf\u0995\u09cd\u09b7\u09c7\u09aa\u09a3 \u0995\u09cb\u09a3\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09aa\u09be\u09b2\u09cd\u09b2\u09be \u09b8\u09b0\u09cd\u09ac\u09be\u09a7\u09bf\u0995\u0964<\/span><\/p>\n

\u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995\u09ad\u09be\u09ac\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09be \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/b>(Equation of<\/b> Motion of a Horizontally Thrown Object or Projectile)<\/b><\/h2>\n

\"\"<\/p>\n

\u09a7\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 <\/span>O<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 <\/span>v<\/span>0<\/span> \u09ac\u09c7\u0997\u09c7 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09a6\u09bf\u0995\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09c7\u09aa \u0995\u09b0\u09be \u09b9\u09b2\u09cb [\u099a\u09bf\u09a4\u09cd\u09b0 <\/span>]\u0964 \u09ac\u09be\u09af\u09bc\u09c1\u09b0<\/span> \u09ac\u09be\u09a7\u09be<\/span> \u0993 \u0989\u099a\u09cd\u099a\u09a4\u09be\u09b0 \u09b8\u09be\u09a5\u09c7 <\/span>g<\/span>–<\/span>\u098f\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0985\u0997\u09cd\u09b0\u09be\u09b9\u09cd\u09af \u0995\u09b0\u09b2\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09ac<\/span>\u09b8\u09cd\u09a4\u09c1\u09b0<\/span> \u0997\u09a4\u09bf\u09aa\u09a5\u09c7\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf<\/span>\u0995<\/span> \u09ac\u09c7\u0997<\/span> \u0985<\/span>\u09ad\u09bf\u09a8\u09cd\u09a8 <\/span>\u098f\u09ac\u0982 <\/span>v<\/span>0<\/span> \u09b9\u09ac\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u0996\u09be\u09a1\u09bc\u09be \u0989<\/span>\u09aa\u09be\u0982\u09b6 \u09a8\u09be \u09a5\u09be\u0995\u09be\u09df <\/span>\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u09c0\u09af\u09bc \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09a6\u09b0\u09c1\u09a8 \u0996\u09be\u09a1\u09bc\u09be \u09a8\u09bf\u099a\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7<\/span> \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09c7 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09ac\u09c7\u0964 \u09a7\u09b0\u09bf <\/span>t<\/span> \u09b8\u09c7<\/span>\u0995\u09c7\u09a8\u09cd\u09a1\u09c7 <\/span>\u09aa\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09a6\u09bf\u0995\u09c7 <\/span>x<\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0993 \u0996\u09be\u09a1\u09bc\u09be \u09a8\u09bf\u099a\u09c7\u09b0 \u09a6\u09bf<\/span>\u0995\u09c7 <\/span>y<\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u09b2 \u098f\u09ac\u0982 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/span>\u09a4\u09c7 <\/span>\u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u09ac\u09c7\u0997 <\/span>v<\/span> \u0993 <\/span>v<\/span> –<\/span>\u098f\u09b0 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u0993 \u0989\u09b2\u09cd\u09b2\u09ae\u09cd\u09ac\u00a0 \u0985\u0982\u09b6\u0995\u09c7\u09b0 <\/span>\u09ae\u09be\u09a8\u0964 <\/span>\u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>v<\/span>x<\/span> \u0993 <\/span>v<\/span>y<\/span>\u0964<\/span> \u09a4\u09be\u09b9\u09b2\u09c7,<\/span><\/p>\n

v<\/span>x<\/span>=<\/span>v<\/span>0<\/span>=<\/span><\/p>\n

\u0993\u00a0 <\/span>v<\/span>y<\/span>=0+gt=gt=<\/span><\/p>\n

\u2234v=<\/span>v<\/span>x<\/span>2<\/span>+<\/span>v<\/span>y<\/span>2<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 <\/span>v<\/span> -\u098f\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8 <\/span>\u03b8<\/span>\u0964<\/span><\/p>\n

\u2234<\/span>tan<\/span> =<\/span>v<\/span>y<\/span>v<\/span>x<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0 <\/span>,<\/span>\u00a0x=<\/span>v<\/span>0<\/span>\u00d7t<\/span> \u2026 \u2026 \u2026 (3) <\/span>[<\/span> \u0985\u09a8\u09c1\u09ad\u09c1\u09ae\u09bf\u0995\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>=0]<\/span><\/p>\n

\u0993 <\/span>y=<\/span>1<\/span>2<\/span>g<\/span>t<\/span>2<\/span> \u2026 \u2026 \u2026 (4) <\/span>[<\/span> \u0989\u09b2\u09cd\u09b2\u09ae\u09cd\u09ac <\/span>\u09a6\u09bf\u0995\u09c7 \u0986\u09a6\u09bf \u09ac\u09c7\u0997 <\/span>=0]<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(<\/span>3)<\/span> \u09b9\u09a4\u09c7 <\/span>t<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(4<\/span>)<\/span>–<\/span>\u098f \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc-<\/span><\/p>\n

y=<\/span>1<\/span>2<\/span>g<\/span>x<\/span>v<\/span>0<\/span>2<\/span><\/p>\n

\u2234<\/span>x<\/span>2<\/span>=<\/span>2<\/span>v<\/span>0<\/span>2<\/span>8<\/span>y<\/span><\/p>\n

\u0989\u09aa\u09b0\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 <\/span>2<\/span>v<\/span>0<\/span>2<\/span>g<\/span>=4A<\/span> \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc<\/span>,<\/span><\/p>\n

x<\/span>2<\/span>=4Ay<\/span><\/p>\n

\u098f\u099f\u09bf \u098f\u0995\u099f\u09bf \u0985\u09a7\u09bf\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964 \u0995\u09be\u099c\u09c7\u0987 \u09ac\u09be\u09a7\u09be\u09b9\u09c0\u09a8 \u09aa\u09a5\u09c7 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995\u09ad\u09be\u09ac\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09be \u09aa\u09cd\u09b0\u09be\u09b8\u09c7\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5 \u09aa\u09cd\u09af\u09be\u09f1\u09be\u09ac\u09cb\u09b2\u09be (<\/span>Parabola)<\/span> \u09ac\u09be \u0985\u09a7\u09bf\u09ac\u09c3\u09a4\u09cd\u09a4 \u09b0\u099a\u09a8\u09be \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u09a4\u09c1\u09ae\u09bf \u09af\u09a6\u09bf \u09b8\u09cd\u099f\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09ae\u09c7 \u0995\u0996\u09a8\u0993 \u0995\u09cd\u09b0\u09bf\u0995\u09c7\u099f \u0996\u09c7\u09b2\u09be \u09a6\u09c7\u0996\u09a4\u09c7 \u09af\u09be\u0993 \u09a4\u09be\u09b9\u09b2\u09c7 \u09ac\u09be\u0989\u09a8\u09cd\u09a1\u09be\u09b0\u09bf \u09a5\u09c7\u0995\u09c7 \u099b\u09cb\u0981\u09a1\u09bc\u09be \u0995\u09cd\u09b0\u09bf\u0995\u09c7\u099f \u09ac\u09b2\u09c7\u09b0 \u0997\u09a4\u09bf \u09b2\u0995\u09cd\u09b7 \u0995\u09b0\u09b2\u09c7 \u09a6\u09c7\u0996\u09ac\u09c7 \u09ac\u09b2\u099f\u09bf \u09aa\u09cd\u09b0\u09a5\u09ae\u09c7 \u09ad\u09c2\u09ae\u09bf \u09a5\u09c7\u0995\u09c7 \u0989\u09aa\u09b0\u09c7 \u0993\u09a0\u09c7 \u09aa\u09c1\u09a8\u09b0\u09be\u09af\u09bc \u09ac\u09be\u0981\u0995\u09be \u09aa\u09a5\u09c7 \u09ad\u09c2\u09ae\u09bf\u09a4\u09c7 \u09ab\u09bf\u09b0\u09c7 \u0986\u09b8\u09c7\u0964 \u0986\u09ac\u09be\u09b0 \u09ac\u09a8\u09cd\u09a6\u09c1\u0995 \u09a5\u09c7\u0995\u09c7 \u0989\u09aa\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u099b\u09cb\u09a1\u09bc\u09be \u09ac\u09c1\u09b2\u09c7\u099f\u09c7\u09b0 \u0997\u09a4\u09bf, \u09a8\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09a4\u09c0\u09b0<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[50,3028,51],"tags":[3887,3554,3888,3889],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/10609"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=10609"}],"version-history":[{"count":4,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/10609\/revisions"}],"predecessor-version":[{"id":10613,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/10609\/revisions\/10613"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=10609"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=10609"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=10609"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}