Question

A swimmer wishes to cross a $500\text{m}$ wide river flowing at a rate of $2m/s$. His speed with respect to still water is $4m/s$. What angle (in degrees) should the swimmer make with the vertical so that he reaches the exact opposite of the point of his start?

• A. $0^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$


When the swimmer starts swimming in the river, the velocity of the river pushes him towards the right. Hence he should make an angle towards the left of the vertical, so that he reaches the exact opposite point to the point of start.
For drift $x$ to be zero, the magnitude of $x$ component of the velocity of the swimmer w.r.t. to the still river should be equal to the magnitude of velocity of the river.
Hence, $4\sin \theta =2\Rightarrow \theta ={30}^{\circ }$
Hence the correct option is (d).