A swimmer can swim in still water at a rate 4.0 km/h. If he swims in a river flowing at 3.0 km/h and keeps his direction (with respect to water) perpendicular to the current, find his velocity with respect to ground.

5.0 km/h

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7.0 km/h

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9.0 km/h

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11.0 km/h

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Solution

The correct option is B 5.0 km/h
The velocity of the flow of river with respect to ground is $= {\to v}_{R} = 3 k m / h^i$
The velocity of swimmer with respect to river= ${\to v}_{S R} = 4 k m / h^j$
Hence the velocity of swimmer with respect to ground= ${\to v}_{R} + {\to v}_{S R} = 3 k m / h^i + 4 k m / h^j$
Hence the magnitude of this velocity is $\sqrt{3^{2} + 4^{2}} k m / h$
$= 5 k m / h$

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