Question

A man is moving with speed 3 km/hr along horizontal
Road, Rain appears to be falling vertically downward
When he stops, Rain appear to be falhyg at an angle 37°
with vertical. Calculate speed (in km/h) of rain appear to
man when he is in motion,​

Answer 1

Answer:

THERE IS YOUR amswer :-

To man walking a the rate of 3km/h the rain appears to fall vertically

When he increases his speed to 

=6km/h it appears to meet him at an angle of 45° with verticl.

Find the velocity the rain.

Solution 

Let i^ and j^ be unit vector in horizontal and vertical respectively

Let, velocity of rain vr=ai^+bj^

Speed off the rain=a2+b2

Case 1

When the relative velocity of rain with respect to man is vertical

vrms=vr−vmvm=3i^vrms=(a−3)i^+bj^

Since vrms is vertical

a+3=0⇒a=3

Case 2

When relative velocity is at 45°

m=6i^vrms=(a−6)i^+bj^=3i^+bj^

And since tanθ=−3b

tan45°=1

∣b∣=3

Therefore speed=33+32=32