Ball `1` is released from the top of a smooth inclined plane, the at the same instant ball `2` is projected from the foot of the plance with such a velocity that they meet halfway up the incline. Determine:
a.the velocity with which balls are projected and
b. the velocity of each ball when they meet.
.

Explanation

For ball 1: `u_(1)=0, a=g sun theta=g ((h)/(l))` and `s=l//2`
Using `v^(2)=u^(2)+2as rArr v^(2)=0+2g ((h)/(l)).((1)/(2))`
`rArr v=sqrtgh`
Again using `v=u+at rArr v=0+g ((h)/(l)).t`
`sqrtgh=g ((h)/(l))t rArr t=(l)/(sqrtgh)`
For nall 2: `u=u_(2), v=v_(2)` and `a=-g sin theta=-((h)/(l))`
Using `v^(2)=u^(2)2as rArr v_(2)^(2)=u_(2)^(2)+2(-g(h)/(l)).((l)/(2))` ...(iii)
Asing using `v=u+at rArr v_(2)=u_(2)-(g(h)/(l)).(l)/(sqrtgh)` ...(iv)
Form (iii) and (iv) `u_(2)=sqrtgh and v_(2)=0`
Hence velocity of ball `2` at the of throwing will be and when it meets ball `1` its velocity becomes zero.
The velocity of ball `1` when it meets ball `2` is `sqrtgh`.