Question

A man is running with 6m/s with his umbrella held vertically. If he doubles his speed he holds the umbrella at 30 degree with vertical.find the speed and direction of rain

Answer 1

$v_m=2\times 6=12ms^{-1}\\ \tan30\degree=\dfrac{12}{v_{rm}}\\ \\ {v_{rm}}=12\sqrt{3}ms^{-1}\\ v_r=\sqrt{v_m^2+v_{rm}^2}\\ v_r=\sqrt{12^2+(12\sqrt{3})^2}=24ms^{-1}\\ \theta+30\degree=90\degree\\ \theta=60\degree\\$

Rain speed is 24 metres per second in the direction 60 degrees East of South