question_answer

A person swims in a river aiming to reach exactly opposite point on the bank of a river. His speed of swimming is 0.5 m/s at an angle \[120{}^\circ \] with the direction of flow of water. The speed of water in stream is: [AIPMT 1999]

A) 1.0 m/s

B) 0.5 m/s

C) 0.25 m/s

D) 0.43 m/s

Correct Answer: C

Solution :

Let u be the speed of stream and v the speed of person starts from A and wants to reach at point B directed opposite to A.

As given, v makes an angle of \[120{}^\circ \] with direction of flow u, the resultant of v and u is along AB. From figure

\[u=v\sin \theta =v\sin \,{{30}^{o}}\]

\[\therefore \]      \[u=\frac{v}{2}=\frac{0.5}{2}\] \[(v=0.5\,m/s)\]

\[=0.25\text{ }m/s\]