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:

  1. 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

$$ \begin{aligned} \sin \theta & =\frac{v _r}{v _{s r}}=\frac{2 km / h}{4 km / h}=\frac{1}{2} \Rightarrow \theta=30^{\circ} \\ \text { Clearly, } \quad \alpha & =90^{\circ}+30^{\circ}=120^{\circ} \end{aligned} $$



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