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Motion in a Plane
Relative Velocity in Two Dimensions
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Concepts tested
- crossing a river along the shortest path
All Questions
2019 1 question
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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:$\vec{V}_{SG}=\vec{V}_{SR}+\vec{V}_{RG}$, with $V_{SR}=20\ m/s$ and $V_{RG}=10\ m/s$ (due east). For the shortest path, the resultant velocity must be due north, so the swimmer must head at angle $\theta$ west of north such that $\sin\theta=\frac{V_{RG}}{V_{SR}}=\frac{10}{20}=\frac{1}{2}$ $\theta=30^\circ$ west