At t=0 a ball is thrown straight upward from the ground level at speed Vo. At the same instant, a distance D above, a ball is thrown straight downward, also at speed Vo.

Where do the balls collide in terms of D, Vo, and g?

1) Upward motion

y1 = Vo*t - g (t^2) / 2

2) Downward motion

y2 = D - [Vo*t + g (t^2) / 2]

3) Collision = > y1 = y2

y1 = Vo*t - g (t^2) / 2

y2 = D - [Vo*t + g (t^2) / 2]

Vo*t - g (t^2) / 2 = D - [Vo*t + g (t^2) / 2]

Vo*t - g (t^2) / 2 = D - Vo*t - g (t^2) / 2

D = 2Vo*t = > t = D / (2Vo)

Substitute the value of t in the equation of y1 (it is the same if you do it in the equation of y2)

y1 = Vo*t - g (t^2) / 2 = Vo [D / (2Vo) ] - g [D / (2Vo) ]^2 / 2

y1 = D/2 - g (D^2) / 8 (Vo ^2)

Answer: y1 = D/2 - g (D^2) / 8 (Vo ^2)