I'm going to make a few assumptions like a hockey ball and a hockey puck are the same thing. ;-) Also, the initial speed of the basketball is X, and third, I'll ignore air resistance.

Obviously, the B-ball and the puck will not hit the ground at the same time, in fact, the puck will hit the ground first. Let's assume the speed of the puck when it hits the ground is Y.

Because the acceleration due to gravity is a constant we can say the speed of the B-ball when it hits the ground is X + Y.

Why? Because by the time the B-ball goes up and comes back down to the original height from whence it was released and the puck dropped, the acceleration due to gravity will have the B-ball going exactly the same speed only in the opposite direction.

(Please note I am talking about speeds here. I am intentionally leaving out the direction required for velocities. Hopefully, this will be more clear than trying to assign negative velocities to things going up and positive velocities to things going down as physicists are so want to do.)

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