A river of width 100 m flows east at 3 m/s. A boat can move at 5 m/s relative to water. A target on the opposite bank starts directly opposite the boat and moves east at 1 m/s. To hit the moving target, the westward component of the boat's velocity relative to water must be:
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Question

A river of width 100 m flows east at 3 m/s. A boat can move at 5 m/s relative to water. A target on the opposite bank starts directly opposite the boat and moves east at 1 m/s. To hit the moving target, the westward component of the boat's velocity relative to water must be:

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G1 Physics · Accepted Answer

The boat and target must have the same eastward ground-velocity component. Let the required boat-relative-water westward component be w. Then 3 - w = 1, so w = 2 m/s. The remaining cross-river component is √(5² - 2²) = √21 m/s, so the meeting is feasible.