Question

a man is walking in rain with an umbrella in his hand.rain is falling vertically downwards with a velocity of vr and the man is walking horizontally horizontally with a velocity vm.at what angle should he hold the umbrella in order to protect himself from getting wet.

Answer 1

$$\begin{gathered} Theresul\tan tvelocityoftherainandthemanis, \\ V=\sqrt{{v_r}^2+{v_m}^2} \\ Theanglemadebythedirectionofrainwithdirectionofresul\tan tvelocityis, \\ \theta =\frac{v_r}{\sqrt{{v_r}^2+{v_m}^2}}. \\ Thereforethemanmustholdhisumbrellaatanangle\theta =\frac{v_r}{\sqrt{{v_r}^2+{v_m}^2}}withthevertical \\ intheupwarddirection. \end{gathered}$$