Up and Down - Futility Closet

Up and Down

A remarkably simple question by Russian scientist A. Savin, from the September/October 1995 issue of Quantum:

A ping-pong ball is tossed into the air. Will it take longer to go up or to come back down?

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The ball is always working against air resistance, so it’s losing energy all the time; at a given height, its total energy while rising is greater than while falling. The ball’s potential energy at this height is the same in both cases, so its kinetic energy (and hence its speed) is greater when it’s rising. So it takes longer to fall than to rise.