Question

A man while running with the speed of 8m/s holds his umbrella vertically to protect himself , if he increases his speed by 50 percent, he has to hold his umbrella 30 degree with vertical. Find speed and direction of rain.

Answer 1

$v_m=\dfrac{150}{100}\times8=12ms^{-1}\\ \tan30\degree=\dfrac{12}{v_{rm}}\\ \\ {v_{rm}}=12\sqrt{3}ms^{-1}\\ v_r=\sqrt{v_m^2+v_{rm}^2}\\ v_r=\sqrt{12^2+(12\sqrt{3})^2}=24ms^{-1}\\ \theta+30\degree=90\degree\\ \theta=60\degree\\$

Speed of rain is 24 metres per second 60 degrees South of East