Question

A man at rest observes that rain is falling vertically downwards. When he moves with a velocity of $3\text{km/h}$, he holds an umbrella at an angle of ${37}^{\circ }$ from the vertical to avoid rain. The velocity of the rain with respect to man is

• A. $8\text{km/h}$
• B. $7\text{km/h}$
• C. $6\text{km/h}$
• D. $5\text{km/h}$

Answer 1

The correct option is D $5\text{km/h}$

As the man holds the umbrella at ${37}^{\circ }$ to the vertical, the velocity of rain with respect to man is acting at that angle.


From this we can get $V_{R,M}$ as,
$\sin {37}^{\circ }=\frac{V_M}{V_{R,M}}$
$V_{R,M}=\frac{V_M}{\sin {37}^{\circ }}$

$V_{R,M}=\frac{3\times 5}{3}=5km/h$