Question

A man is walking at a speed $3m/s$ rain drops are falling vertically with a speed $3m/s$:
(i) What is the velocity of rain drop with respect to the man?
(ii) At what angle from vertical, the man should hold his umbrella?

• A. $2.42m/s,{30}^{\circ }$ in forward direction
• B. $4.24m/s,{45}^{\circ }$ in forward direction
• C. $1.24m/s,{60}^{\circ }$ in forward direction
• D. None of the above

Answer 1

The correct option is B $4.24m/s,{45}^{\circ }$ in forward direction

Relative velocity $v=\sqrt{v_x^2+v_y^2}=\sqrt{3^2+3^2}=3\sqrt{2}=4.24m/s$

$\theta =ta{n}^{-1}\frac{v_y}{v_x}=ta{n}^{-1}\frac{3}{3}={45}^o$