A man standing on a road holds his umbrella at 30∘ with the vertical to k

Question

A man standing on a road holds his umbrella at

30^{\circ}

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

Options:

A . 10 km/hr

B . 20 km/hr

C . 30 km/hr

D . 40 km/hr

Answer: Option B
:
B
When the man is at rest w.r.t the the ground, the rain comes to him at an angle

30^{\circ}

with the vertical. This is the direction of the velocity
of raindrops with respect to the ground.
Here

{⃗ v}_{r g}

= velocity of rain with respect to the ground

{⃗ v}_{m g}

= velocity of the main with respect to the ground
and

{⃗ v}_{r m}

= velocity of the rain with respect to the man.
We have

{⃗ v}_{r g}

{⃗ v}_{r m}

{⃗ v}_{m g}

... (i)

{⃗ v}_{r g}

sin

30^{\circ}

{⃗ v}_{m g}

= 10 km/hr
or

{⃗ v}_{r g}

\frac{10}{s i n 30^{\circ}}

= 20 km/hr

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