Question

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 :
(1) 30° west
(2) 0°
(3) 60° west
(4) 45° west

Answer 1

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Answer 2

The angle at which he should make his strokes w.r.t. north is given by $\bold{30^{o}}$ west.

Step by step explanation:

From the given,

The speed of a swimmer in still water  = $V_{SR}$ = 20 m/s.

The speed of river water = $V_{RG}$ =  10 m/s

             $\bold{V_{SG}= \overrightarrow{V}_{SR}+\overrightarrow{V}_{RG}}$........................(1)

From the graph(attachment)

            $\bold{Sin\Theta =\frac{\overrightarrow{V}_{RG}}{\overrightarrow{V}_{SR}}}$................................(2)

Substitute the given values in equation (2)

                        $\Rightarrow \frac{10}{20}$

                       $\Rightarrow Sin\Theta = \frac{1}{2}=30^{0}$

Therefore, The angle at which he should make his strokes w.r.t. north is given by $\bold{30^{o}}$ west.

Correct answer - 1