Question

a man walking at the rate of 2 km/hour with respect to ground, the rain appears to fall vertically. When
To a man walk
he increases his speed to 4 km/hour in same direction of his motion, rain appears to meet him at an angle
of 45° with horizontal, find the real direction and speed of the rain.​

Answer 1

Explanation:

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

Let velocity of rain vr=ai^+bj^

speed of rain=a2+b2

Case I:

when relative velocity of rain w.r.t man is vertical

vrm=v¯r−v¯m

vm=3i^

vrm=(a−3)i^+bj^

Since vrm is vertical

a−3=0=>a=3

Case II:

when relative velocity is at 45∘