Rain, driven by the wind, falls on a railway compartment with a velocity of 20 ms-1 , at an angle of 30o to the vertical. The train moves, along the direction of wind flow, at a speed of 108 km h-1. Determine the apparent velocity of rain for a person sitting in the train.

Speed of train =108×518=30ms−1Let v→R and v→T represent the respective velocities of rain and train.Now, the relative velocity of rain w.r.t. person (train) is given by vR,T=v→R−v→T⇒v→R+−v→TLet OR→ and RT→ represent the vectors, respectively, in magnitude and direction.OT2=OR2+RT2+2OR⋅RTcos⁡120∘=202+302−2×20×30×12=400+900−600=700=700ms−1=107ms−1