Someone standing at the edge of a cliff throws one ball straight up and another ball straight down

A person standing at the edge of a cliff throws one ball straight up and another ball straight down at the same initial speed. Neglecting air resistance, the ball which hits the ground at the base of the cliff with the greater speed is the one initially thrown:

 

Answer

It will hit at the same time. I didn't read question correctly at first. I was assuming you dropped one ball and threw one up in the air. But in this problem you are throwing one ball down with a velocity beyond gravity force. So what happens is the same initial velocity given to both balls is added to by the force of gravity for the one falling down and the one that is thrown upwards trades it's upward kinetic energy for gravitational potential energy and so when it reaches it's peak it will have the additional vertical distance to accelerate to equal the velocity of the ball thrown down.