A stone falling from the top of a vertical tower has descended `x` metre when another is dropped from a point `y` metre, below the top. If they fall from rest and from rest andreach the groundtogerher, show that the height of the tower is `(x+y)^(2))/(4x) m`.

Answer

`((x+y))^(2)/(4 x)`

Explanation

Time taken by first stone to fall through `h-x` is equal to time taken by second stond stone to fall through `h-y`.
`h-y =(1)/(2) g t^(2), u_(1)=sqrt 2gx`
`h-x=u_(1)t +(1)/(2) g t^(2)`
Solve to get `h=((x+y)^(2))/(4x)`
.