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?

A ball thrown in vertically upward direction attains maximum height of

1.	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» 15 m 6m 12 m 9m Solution :For motion of a ball in VERTICALLY upward direction, suppose`v _(0) = ` initial velocity = ?. v = velocity at maximum height `(20 m) =0. ` `a =- G and d = 20 m` From equation `2d=v _(2) -v _(0) ^(2) ,` we GET, `- 2g xx 20 = (0) ^(2) -v _(0) ^(2)` `therefore - 40 g=- v_(0) ^(2)` `therefore v _(0) ^(2) = 40 g ""...(1)` Now, suppose velocity at height `h = v = (v _(0))/(2)` ` therefore` From equation `2 ad = v ^(2) -v _(0) ^(22),` we get, `- 2 gh = (v _(0) ^(2))/( 4) = (because a=-g, d = h, v = (v _(0))/(2))` `therefore -2gh =- ( 3v _(0) ^(2))/( 4)` `therefore -h = ( 3v _(0) ^(2))/( 4 xx 2g)` `therefore h = (3 xx 40 g)/(8g)` (From eq. (i)) `therefore h = 15m`