question_answer

Rain is falling vertically with a speed of\[4\,m{{s}^{-1}}\]. After some time, wind starts blowing with a speed of \[3\,m{{s}^{-1}}\]in the north to south direction. In order to protect himself from rain, a man standing on ground should hold his umbrella at an angle \[\theta \] given by

A)  \[\theta ={{\tan }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards South

B)  \[\theta ={{\tan }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards North

C)  \[\theta ={{\cot }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards South

D)  \[\theta ={{\cot }^{-1}}\,\left( \frac{3}{4} \right)\] with the vertical towards North

Correct Answer: A

Solution :

 Resultant velocity of rain \[v={{v}_{r}}+{{v}_{w}}=3i+4j\] \[\therefore \] \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\] As wind is blowing from south, umbrella should be hold towards south.