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A ball thrown in vertically upward direction attains maximum height of 20 meter. At what height would its velocity be half of its initiall velocity?

Answer» <html><body><p>15 m <br/>6m <br/>12 m <br/>9m </p>Solution :For motion of a ball in <a href="https://interviewquestions.tuteehub.com/tag/vertically-3260386" style="font-weight:bold;" target="_blank" title="Click to know more about VERTICALLY">VERTICALLY</a> upward direction, suppose`v _(0) = ` initial velocity = ?. <br/> v = velocity at maximum height `(20 m) =0. ` <br/> `a =- <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a> and d = 20 m` <br/> From equation `2d=v _(2) -v _(0) ^(2) ,` we <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a>, <br/> `- 2g xx 20 = (0) ^(2) -v _(0) ^(2)` <br/> `therefore - 40 g=- v_(0) ^(2)` <br/> `therefore v _(0) ^(2) = 40 g ""...(1)` <br/> Now, suppose velocity at height `h = v = (v _(0))/(2)` <br/> ` therefore` From equation `2 ad = v ^(2) -v _(0) ^(22),` we get, <br/> `- 2 gh = (v _(0) ^(2))/( <a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>) = (because a=-g, d = h, v = (v _(0))/(2))` <br/> `therefore -2gh =- ( 3v _(0) ^(2))/( 4)` <br/> `therefore -h = ( 3v _(0) ^(2))/( 4 xx 2g)` <br/> `therefore h = (<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a> xx 40 g)/(8g)` (From eq. (i)) <br/> `therefore h = 15m`</body></html>


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