# question answer

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 means how man sees the velocity of rain.

Vrm = Vr – Vm

Vm = 10 i

Vrm = (a i+ b j)- 10 i

= (a-10)i + b j

Since Vrm is vertical, the horizontal component is zero.

so, a-10 = 0, a= 10

Case II:

when relative velocity is at 60′

Vm = 20 i

Vrm = (a-20) i + b j

= -10 i + b j

And tan theta = b/ a = b/ -10

tan 60′ = √3 = b/ -10

so, b = -10*√3

Now we have both the a and b value, so, let’s count velocity of rain = √a2 + b2

= √(10)2 +(-10√3)2

= √400 = 20 m/s