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 \[{{120}^{\text{o}}}\] with the direction of flow of water. The speed of water in stream is:

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 \[{{120}^{\text{o}}}\] 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 m/s