Question

Rain is falling vertically with a speed of `35 m s^(-1)` . A woman rides a bicycle with a speed of ` 12 m s^(-1)` in east to west direction. In which direction should she hold her umbrella ?
A. `sin^(-1)((12)/(35))`
B. `cos^(-1)((12)/(35))`
C. `tan^(-1)((12)/(35))`
D. `cot^(-1)((12)/(35))`

Answer 1

Correct Answer - C
The velocity of the rain and the wind are represented by the vectors `vecv_(r)` and `vecv_(w)` as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity `vecv_(R)` . If `theta` is the angle which reusltant velocity `vecv_(R)` makes with the vertical, then
`tan theta = (v_(w))/(v_(r)) = (12)/(35) or theta = tan^(-1) ((12)/(35))`