# Rain is falling vertically with a speed of 20ms –1 . A person isrunning in the rain with a velocity of 5 ms –1 and a wind is alsoblowing with a speed of 15ms-1 (both from the west). What isthe angle with the vertical at which the person should hold hisumbrella so that he may not get drenched.

Harsh Tiwari
54 Points
one year ago
The velocity of the rain that is vertically falling downward is v(rain)
​=20m/s.
The velocity of the wind that is blowing from west to east is v(wind)
​=15m/s
as the person is walking 5m/s, hence, the final velocity from west to east is =10m/s
Now, the resultant velocity
v makes an angle θ with the vertical.
tanθ= v(rain)/v(wind)
=10/20
tan$\Theta$=1/2