{"id":261335,"date":"2022-09-10T12:37:13","date_gmt":"2022-09-10T07:07:13","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-ball-of-mass-m-is-moving-towards-a-batsman-at-a-speed-v-the-batsman-strikes-the-ball-and-deflects-it-by-an-angle-%ce%b8-without-changing-its-speed-the-impulse-imparted-to-the-ball-is-giv\/"},"modified":"2022-09-10T12:37:13","modified_gmt":"2022-09-10T07:07:13","slug":"a-ball-of-mass-m-is-moving-towards-a-batsman-at-a-speed-v-the-batsman-strikes-the-ball-and-deflects-it-by-an-angle-%ce%b8-without-changing-its-speed-the-impulse-imparted-to-the-ball-is-giv","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-ball-of-mass-m-is-moving-towards-a-batsman-at-a-speed-v-t\/","title":{"rendered":"A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle\u00a0\u03b8\u00a0without changing its speed. The impulse imparted to the ball is given by"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle\u00a0\u03b8\u00a0without changing its speed. The impulse imparted to the ball is given by","custom_permalink":"question\/physics\/a-ball-of-mass-m-is-moving-towards-a-batsman-at-a-speed-v-t\/"},"categories":[],"acf":{"question":"

A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle \u03b8<\/mi><\/math> without changing its speed. The impulse imparted to the ball is given by<\/p>","options":[{"option":"

mv<\/mi> <\/mo>cos<\/mi> <\/mo>\u03b8<\/mi><\/mfenced><\/math><\/p>","correct":false},{"option":"

mv<\/mi> <\/mo>sin<\/mi> <\/mo>\u2061<\/mo>(<\/mo>\u03b8<\/mi>)<\/mo><\/math><\/p>","correct":false},{"option":"

2<\/mn> <\/mo>mv<\/mi> <\/mo>cos<\/mi> <\/mo>\u2061<\/mo>\u03b8<\/mi>2<\/mn><\/mfrac><\/mfenced><\/math><\/p>","correct":true},{"option":"

2<\/mn> <\/mo>mv<\/mi> <\/mo>sin<\/mi> <\/mo>\u2061<\/mo>\u03b8<\/mi>2<\/mn><\/mfrac><\/mfenced><\/math><\/p>","correct":false}],"solution":"

The ball moving along AB with velocity v is deflected along BC with velocity v'. The magnitude of vectors v and v' is the same = v.
Change in velocity is \u0394<\/mi>v<\/mi>=<\/mo>v<\/mi>\u2032<\/mi><\/msup>\u2212<\/mo>v<\/mi>=<\/mo>v<\/mi>\u2032<\/mi><\/msup>+<\/mo>(<\/mo>\u2212<\/mo>v<\/mi>)<\/mo><\/math>, i.e.,\u2206<\/mo>V<\/mi><\/math> is the resultant of vectors v' and -v. As shown in figure, the magnitude of \u2206<\/mo>V<\/mi><\/math> is given by 
\u0394v<\/mi>=<\/mo>v<\/mi>2<\/mn><\/msup>+<\/mo>v<\/mi>2<\/mn><\/msup>+<\/mo>2<\/mn>v<\/mi>2<\/mn><\/msup>cos<\/mi>\u2061<\/mo>\u03b8<\/mi><\/msqrt> <\/mspace> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo>=<\/mo>2<\/mn>v<\/mi>2<\/mn><\/msup>(<\/mo>1<\/mn>+<\/mo>cos<\/mi>\u2061<\/mo>\u03b8<\/mi>)<\/mo><\/msqrt> <\/mspace> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo>=<\/mo>2<\/mn>v<\/mi> <\/mo>cos<\/mi> <\/mo>\u2061<\/mo>\u03b8<\/mi>2<\/mn><\/mfrac><\/mfenced><\/math>
 <\/p>
<\/figure>
<\/figure>","subject":""},"yoast_head":"\nA ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle\u00a0\u03b8\u00a0without changing its speed. The impulse imparted to the ball is given by - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle\u00a0\u03b8\u00a0without changing its speed. 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