Question 155: Motion in 2D & Vectors

Question

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)

Accepted Answer

The situation is depicted in the following figure.
where, V
MR
= velocity of man = 12 km/h
and v
R
= velocity of water flow in river = 6 km/h
As, v
MR
should be along CD.
$$ \Rightarrow {v_R} - {v_{MR}}\sin 	heta  = 0$$
$$ \Rightarrow 6 - 12\sin 	heta  = 0 \Rightarrow \sin 	heta  = {6 \over {12}}$$
$$ \Rightarrow \sin 	heta  = {1 \over 2}$$
$$ \Rightarrow 	heta  = {\sin ^{ - 1}}\left( {{1 \over 2}} ight) = {\sin ^{ - 1}}(\sin 30^\circ )$$ [$$\because$$ $$\sin 30^\circ  = {1 \over 2}$$]
$$ \Rightarrow 	heta  = 30^\circ $$
$$	herefore$$ $$\alpha  = 90^\circ  + 	heta  = 90^\circ  + 30^\circ  = 120^\circ $$
$$ \Rightarrow \alpha  = 120^\circ $$

Motion in 2D & Vectors

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