A juggler throws balls vertically upward at equal time intervals τ with the same speed u. Suppose 2u/(gτ)=N, where N is an integer. If a returning ball is caught just before a new ball is thrown, the number of balls simultaneously in air immediately after each throw is:
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Question

A juggler throws balls vertically upward at equal time intervals τ with the same speed u. Suppose 2u/(gτ)=N, where N is an integer. If a returning ball is caught just before a new ball is thrown, the number of balls simultaneously in air immediately after each throw is:

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G1 Physics · Accepted Answer

The flight time of each ball is T = 2u/g = Nτ. A ball thrown N intervals earlier is caught just before the new throw. Immediately after a throw, the balls in air have ages 0, τ, 2τ, ..., (N−1)τ. Hence the number of balls in air is N.