Aball with a horizontal speed of 1.0m/s rolls off a bench 2.0 m high. (a) how long will the ball take to reach the floor? (b) how far from a point on the floor directly below the edge of the bench will the ball land?

The motion of the ball is a composition of two motions:
- on the x (horizontal) axis, it is a uniform motion with initial velocity 
- on the y (vertical) axis, it is a uniformly accelerated motion with acceleration  

(a) to solve this part, we just analyze the motion on the vertical axis. The law of motion here is

By requiring y(t)=0, we find the time t at which the ball reaches the floor:



(b) for this part, we can analyze only the motion on the horizontal axis. To find how far the ball will land, we must calculate the distance covered on the x-axis, x(t), when the ball reaches the ground (so, after a time t=0.64 s):