Question

To a man walking at the rate of 3km/hour the rain appears to fall vertically downward.
When he increases his speed to 6 km/hour, it appears to meet him at an angle of 30 degree with
the downward vertical. Find the real direction and speed of rain as seen by a stationary observer.

Answer 1

=> Suppose, i^ and j^ be unit vector in horizontal and vertical respectively.

now, velocity of rain v_r = ai^ + bj^

speed of rain= √a2+b2

(I):  when relative velocity of rain with respect to man is vertical

v_rm = v¯r − v¯m

v_m = 3i^

v_rm = (a − 3) i^ + bj^

As v_rm is vertical

a−3 = 0

=> a = 3

( II ):  when relative velocity is at 30⁰

Velocity of man, v¯m=6i^

vrm = (a−6)i^ + bj^

=−3i^+bj^

As tanθ=b/−3

tan 30=1/√3

1/√3  =b/−3

=> |b|=3/√3

=> speed = √a² + b²

= √ 3² + (3/√3)²

= 6