Question

to a man walking due east at the rate of 2km/h ,rain drops to fall vertically and when he increase his speed to 4km/h ,it appears to meet him at 45degree find real direction and speed of rain?

Answer 1

Let Vm be the speed of man.
Let V be the speed and Vhor is the horizontal component of the speed
of rain drops, and A be the angle between rain's direction and the normal direction.

Vhor = V·sinA.
Vhor = Vm1 = 2km/h
V·sin45 = Vm2
V = Vm2 / sin45 = 4 / sin45 = 5.6569 km/h
V·sinA = Vm1
A = asin(Vm1/V) = asin(2/5.6569) = asin(0.3536) = 20.7046°.