Question

Rain is falling vertically with a speed of 30m/s, a woman rides a bicycle with a speed of 10m's in east to west direction. What is the relative velocity of rain with respect to the woman?​

Answer 1

Here,

v

c

=Velocity of the cyclist

v

r

=Velocity of falling rain

In order to protect herself from the rain, the women must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the women

v=v

r

+(−v

c

)

v=30+(−10)=20 m/s

tanθ=

v

r

v

c

=

30

10

θ=tan

−1

(

3

1

)

θ≈18°

Hence the women must hold the umbrella towards the south, at angle of nearly 18° with the vertical