Q 11-03-125JEE MainJEE Main 2021 (27 Jul, Shift 2)Medium
A swimmer wants to cross a river from point $A$ to point $B$. Line $AB$ makes an angle of $30^\circ$ with the flow of the river. The magnitude of the velocity of the swimmer is the same as that of the river. The angle $\theta$ with the line $AB$ should be ______$^\circ$, so that the swimmer reaches point $B$.
Numerical value type. Enter your answer.
Answer: 30
Let both speeds be $v$. The resultant must lie along $AB$, so the components perpendicular to $AB$ must cancel.
River velocity makes $30^\circ$ with $AB$: perpendicular component $v\sin30^\circ$.
Swimmer velocity makes $\theta$ with $AB$ on the other side: perpendicular component $v\sin\theta$.
$v\sin\theta = v\sin30^\circ \Rightarrow \theta = 30^\circ$.
Solution by Sreeraj P, M.Sc Physics