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?

Options

A. 15 m
B. 6m
C. 12 m
D. 9m

Answer

A

Explanation

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`