Water drops fall from a tap at equal time intervals. The first drop reaches the ground exactly four time intervals after its release. At that instant a new drop is just released. The successive vertical gaps between the drops, measured upward from the ground, are in the ratio:
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Question

Water drops fall from a tap at equal time intervals. The first drop reaches the ground exactly four time intervals after its release. At that instant a new drop is just released. The successive vertical gaps between the drops, measured upward from the ground, are in the ratio:

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G1 Physics · Accepted Answer

Let the release interval be τ. At the instant the first drop reaches the ground, the ages of the drops are 4τ, 3τ, 2τ, τ, 0. Distances fallen are proportional to 16 : 9 : 4 : 1 : 0. Since the ground is at the level corresponding to 16 units, the heights of the drops above the ground are 0, 7, 12, 15, 16. Therefore successive upward gaps are 7, 5, 3, 1, so the ratio is 7:5:3:1.