A man running on a horizontal road at 8km/hr finds the rain falling vertically. He increases his speed to 12km/hr and finds that the rain drops make an angle of 30 with the vertical.Find the speed and direction of the rain with respect to the road.

Dear Student

This shows that the horizontal component of rain=8km/hras the relative velocity of the rain has only a vertical component with respect the man.
Vx​=8km/hr
2ndcase
→VRM​=VR​−VM​
=(8↑−Vy​↑)−12↑
=−4↑−V_y​↑
tan30^o= 4​ /V_y​
⇒ 1​ / √3 = 4​ /Vy​
Vy​ = 4√3​km/hr

Velocity of Rain= 8km/hr↑−4√3​km/hr↑
⇒tan α = ​2​ / √3 from vertical.


Thanks