Question

-
To a stationary man rain is falling on his back with
a velocity 6 km/h at an angle 30° with vertical. To
make the rain velocity appear vertical the man
should move
(1) Forward with a velocity 3 km/h
(2) Forward with a velocity 3×3^1/2 km/h
(3) Backward with a velocity 3 km/h
(4) Forward with a velocity 2×3^1/2 km/h
​

Answer 1

Given :

Vr = 6km/hr

θ = 30°

To find :

Velocity of man so that rain appears vertical to the man.

Solution :

Vrm = Vr - Vm

Vrm = Vr + (-Vm)

Vrm = -Vr cos30° j + (Vr sin30° - Vm) i

Rain will appear vertical to the man only if the horizontal component will become zero.

Therefore,

Vr sin30° - Vm = 0

Vr sin30° = Vm

sin30° = Vm / Vr

1 / 2 = Vm / 6

Vm = 3km/h

If man will walk forward with a velocity 3km/h then rain velocity will appear vertical to man.