Question

Rain is falling vertically with $3{\text{ms}}^{-1}$ and a man is moving due North with $4{\text{ms}}^{-1}$. In which direction he should hold the umbrella to protect himself from rains?

• A. ${37}^{\circ }$ North of vertical
• B. ${30}^{\circ }$ South of vertical
• C. ${53}^{\circ }$ North of vertical
• D. ${60}^{\circ }$ South of vertical

Answer 1

The correct option is C ${53}^{\circ }$ North of vertical

As man is moving towards north ${\overrightarrow{V}}_m=4\hat{j}$
As rain is falling vertically down ${\overrightarrow{V}}_r=-3\hat{k}$
Velocity of rain wrt man
${\overrightarrow{V}}_{rm}={\overrightarrow{V}}_r-{\overrightarrow{V}}_m=-3\hat{k}-4\hat{j}\tan \beta =\frac{4}{3}\Rightarrow \beta ={53}^{\circ }\text{North of vertical}$