Kinematics 3 Question 1
1. The stream of a river is flowing with a speed of $2 km / h$. A swimmer can swim at a speed of $4 km / h$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?
(2019 Main, 9 April I)
(a) $60^{\circ}$
(b) $120^{\circ}$
(c) $90^{\circ}$
(d) $150^{\circ}$
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Answer:
Correct Answer: 1. (b)
Solution:
- Let the velocity of the swimmer is $v _s=4 km / h$ and velocity of river is $v _r=2 km / h$
Also, angle of swimmer with the flow of the river (down stream) is $\alpha$ as shown in the figure below
From diagram, angle $\theta$ is
$$ \begin{aligned} \sin \theta & =\frac{v _r}{v _{s r}}=\frac{2 km / h}{4 km / h}=\frac{1}{2} \Rightarrow \theta=30^{\circ} \\ \text { Clearly, } \quad \alpha & =90^{\circ}+30^{\circ}=120^{\circ} \end{aligned} $$
