Imagine that the ball on the left is given a nonzero initial velocity in the horizontal direction, while the ball on the right continues to fall with zero initial velocity. What horizontal speed vx must the ball on the left start with so that it hits the ground at the same position as the ball on the right?

vₓ = g/2 x/y

Explanation:

For this exercise, let's find the time it takes for the ball on the right that has zero initial velocity to reach the ground.

y = v₀ t - ½ g t²

t = 2y / g

This is the time it takes for the ball on the right to reach the ground; at this time the ball on the left travels a distance

vₓ = x / t

vₓ = x g / 2y

vₓ = g/2 x/y

Where we assume that x and y are known