JEE MAIN - Physics (2021 - 16th March Evening Shift - No. 23)
A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ____________$$^\circ$$. (Round off to the Nearest Integer) (Find the angle in degrees)
Answer
120
Explanation
The situation is depicted in the following figure.
_16th_March_Evening_Shift_en_23_1.png)
where, VMR = velocity of man = 12 km/h
and vR = velocity of water flow in river = 6 km/h
As, vMR should be along CD.
$$ \Rightarrow {v_R} - {v_{MR}}\sin \theta = 0$$
$$ \Rightarrow 6 - 12\sin \theta = 0 \Rightarrow \sin \theta = {6 \over {12}}$$
$$ \Rightarrow \sin \theta = {1 \over 2}$$
$$ \Rightarrow \theta = {\sin ^{ - 1}}\left( {{1 \over 2}} \right) = {\sin ^{ - 1}}(\sin 30^\circ )$$ [$$\because$$ $$\sin 30^\circ = {1 \over 2}$$]
$$ \Rightarrow \theta = 30^\circ $$
$$\therefore$$ $$\alpha = 90^\circ + \theta = 90^\circ + 30^\circ = 120^\circ $$
$$ \Rightarrow \alpha = 120^\circ $$
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