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 ?

Explanation

Here, velocity of rain , `vecv_(r)=35m//s`
Velocity of wind , `vecv_(w)=12m//s`
Magnitude of resultant velocity
`v_(u)=sqrt(v_(R)^(2)+v_(w)^(2))=sqrt((35)^(2)+(12)^(2))=37m//s`
Let the resultant velocity `vecv_(u)` make an angle `theta` with `vecv_(R)` then
`tan theta=(v_(w))/(v_(R))=(12)/(35)=0.343`
`theta=tan^(-1) (0.343)-19^(@)`
The woman should hold the umbrella in the vertical plane , at an angle of `90^(@)` with the vertical, towards east .