Rain is falling vertically with a speed of `35 ms^(-1)`. Winds starts blowing after sometime with the speed of `12ms^(-1)` in east to west direction. At what angles with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

Options

A. `sin^(-1)(12/35)`
B. `cos^(-1)(12/35)`
C. `tan^(-1)(12/35)`
D. `cot^(-1)(12/35)`

Answer

c

Explanation

The velocity of the rain and the wind are represented by the vectors `vecV_(r) and vecV_(w)` as shown in the fig. To protect himself from the direaction of resultant velocity `vecV_(R)`. If `theta` is the angle which resultant velocity `vecV_(R)` makes with the vertical, then `tan theta=(V_(w))/(V_(r))=12/35` or ` theta= tan^(-1) (12/35)`