Question

If a body is projected vertically up it's velocity decreases to half of its initial velocity at a height 'h' above the ground The maximum height reached by it is ? Ans:4h/3

Answer 1

See the explanation below

Explanation:

Let the initial velocity be `=ums^-1`

The acceleration due to gravity is `g=9.8ms^-2`

Resolving in the upward direction `uarr^+`

The velocity at height `hm` is `=u/2ms^-1`

Applying the equation of motion

`v^2=u^2+2as`

`u^2/4=u^2-2gh`

`2gh=3/4u^2`

`u^2=8/3gh`.............................`(1)`

At the maximum height `v=0`

Let the mximum height de `=ym`

Therefore,

`0=u^2-2gy`

Plugging in the value of equation `(1)`

`8/3gh=2gy`

`y=4/3h`

The maximum height is `=4/3hm`

`QED`