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A ball moving rapidly along a tabletop roll off the edge and falls to the floor. At the exact instant that the first ball rolls off the edge, a second ball is dropped from the same height. Which ball, if either, reaches the floor first? Explain.
a. The rolling ball reaches the floor first because it has an initial velocity and the dropped ball does not.
b. The dropped ball reaches the floor first because its velocity is only in the y-direction.
c. Both balls reach the floor at the same time because they both have the same initial zero y-component of velocity.

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Answer:

c. Both balls reach the floor at the same time because they both have the same initial zero y-component of velocity.

Explanation:

At the point where the moving ball rolls off the edge, it has an initial velocity that is purely horizontal. Its vertical velocity is zero initially. This is the same as if it had been dropped from the same height as the dropped ball.

The effect of its horizontal velocity is to make it land at a point farther from the dropped. However, the time of fall is determined by only the vertical motion which is under gravity, hence an accelerated motion.

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