A ball rolls off a 1.0 m high table and lands on the floor, 3.0 m away from the table. What is the horizontal velocity of the ball just before it hits the floor?

Answer 1

This is a free-fall question. An object in free-fall experiences an acceleration in the y-direction but not in the x-direction. This means that the horizontal velocity does not change.

The first step to solving this problem is finding the time. The TIME is determined by how long it takes the ball to fall 1 m. You can assume that the initial velocity of the ball in the vertical is 0 because it rolls off a table and we generally assume the top of a table is a horizontal partial plane. The equation of motion in the y direction is y = (1/2)g t² solving for t, you get t=√(2y/g)

The second step is recognizing that velocity is distance/time. So the velocity in the horizontal is a constant (no acceleration) so the equation of motion is x = v t. Rearrange and solve for v, v = x/t. You know x (the distance from the table) and t is the time of fall, calculated in step 1.