Question

A man standing on a road has to hold his umbrella at

30° with the vertical to keep the rain away. He throws

the umbrella and starts running at 10 km/h. He finds

that raindrops are hitting his head vertically. Find the

speed of raindrops with respect to (a) the road, (b) the

moving

Answer 1

Answer:

Explanation:

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Answer 2

Given that,

A man standing on a road has to hold his umbrella at  30° with the vertical.

The velocity of a man is 10 km/h.

To find,

The  speed of raindrops with respect to (a) the road, (b) the  moving.

Solution,

From the attached figure, we find that,

$\theta=30^{\circ}$

Velocity of rain wrt ground, $v_{rg}=OB$

Velocity of person wrt ground, $V_{pg}=OA=10\ km/h$

Velocity of rain wrt person, $v_{rp}=OC$

In triangle OCB,

$OB=\dfrac{CB}{\sin30}\\\\OB=\dfrac{10}{(1/2)}=20\ km/h$

So, the speed of rain wrt the road is 20 km/h.

(b) In triangle OCB,

$OB=\dfrac{CB}{\tan30}\\\\OB=\dfrac{10}{(1/\sqrt{3} )}=17.31\ km/h$

So, the speed of rain wrt the moving person is 17.31 km/h.