Question

A man standing on a road has to hold his umbrella at ${30}^o$ with the vertical to keep the rain away. He throws the umbrella and starts running at 10 kmph, He finds that rain drops are hitting his head vertically. The speed of raindrops relative to the ground is:

• A. $10kmph$
• B. $20kmph$
• C. $10\sqrt{3}kmph$
• D. $20\sqrt{3}kmph$

Answer 1

The correct option is B $20kmph$

Velocity of the man $v_m$ running with is $10\hat{i}$

when man run he found that rain falling verticaly hitting his head

Let velocity of rain with respact to man $v_{r/m}=-v\hat{j}$

velocity of rain $v_r=v_{r/m}+v_m=-v\hat{j}kmph+10\hat{i}kmph$

$tan{30}^0=\frac{10}{v}$

$\Rightarrow v=10\sqrt{3}kmph$

we gat $v_r=10\hat{i}-10\sqrt{3}\hat{j}$

magnitude we $v=\sqrt{{10}^2+(10\sqrt{3}{)}^2}=20kmph$

Hence B option is correct