Rain is falling vertically with a speed of 12ms−1.A cyclist is moving east to west with a speed of 12√3ms−1.In order to protect himself from rain at what angle he should hold his umbrella w.r.t vertical.
60∘
→vrain=−12^j,→vcyclist=−12√3^i
∴→vrc=→vr−→vc
= −12^j−(−12√3^i)
= −12^j+12√3^i=12√3^i−12^j
∴tanθ=1212√3=1√3
∴θ=30∘
∴ Since the vrain w.r.t cyclist make an angle of 30∘ with the x axis, he must hold the umbrella at an angle of 60∘ to the vertical.