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Rain is falling vertically with a speed ...

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))`

Text Solution

Verified by Experts

The correct Answer is:
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))`
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