Question

A man is going due east with a velocity of 3km/h. Rain falls vertically downwards with a speed of to 10 km/h. Calculate the angle at which he should hold his umbrella so as to save himself from rain. .​

Answer 1

Let the velocity of rain drops be represented by

v

R

=−4km/h

j

^

and the velocity of man be

v

M

=3km/h

i

^

Hence the velocity of rain drops with respect to man=

v

R

−

v

M

−4km/h

j

^

−3km/h

i

^

The magnitude of this relative velocity=

3

2

+4

2

km/h

=5km/h

Answer 2

Step 1: Velocity of rain and man[Ref. Fig.]

The upward direction is positive.

The right direction is positive.

In the figure CA represent the velocity of man and CB represent the velocity of rain 

Velocity of rain wrt ground Vr=−3j^  Km/hr

Velocity of man wrt ground Vm=4i^   Km/hr

Step 2: Relative velocity of rain w.r.t man 

The relative velocity of rain with respect to man:

Vrm=Vr−Vm

        =−3j^−4i^

∣Vrm∣=(32+42)

∣Vrm∣=5km/h