A man standing on a road hold his umbrella at ${30}^0$ with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/hr. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be

When the man is at rest w.r.t. the ground, the rain comes to him at an angle 30° with the vertical. This is the direction of the velocity of raindrops with respect to the ground.

We have ,${\overrightarrow{\mathrm{v}}}_{\mathrm{rg}}={\overrightarrow{\mathrm{v}}}_{\mathrm{rm}}+{\overrightarrow{\mathrm{v}}}_{\mathrm{mg}}$

When the man is running, rain is falling vertically, 

${\mathrm{v}}_{\mathrm{rg}}\sin {30}^0={\mathrm{v}}_{\mathrm{mg}}=10 \mathrm{km}/\mathrm{h}$

$\Rightarrow {\mathrm{v}}_{\mathrm{rg}}=\frac{10}{\sin 30°}=20 \mathrm{km}/\mathrm{hr}$