Question

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

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

Answer 1

Answer: (C)

${53}^{\circ }$ North of vertical

Let $V_r$ be the velocity of the rain .$V_m$ is the velocity of the man.
$V=V_r+V_m=-3\hat{k}-4\hat{j}\Rightarrow tan\beta =\frac{4}{3}\Rightarrow \beta ={53}^o$ north of vertical.
Thus the man should hold the umbrella to protect himself from rains at ${53}^o$