Kinematics Question 321

Question: A man standing on a road hold his umbrella at 30° 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

Show Answer

Answer:

Correct Answer: B

Solution:

When the man is at rest w.r.t. the ground, the rain comes to him at an angle 30° with the vertical.

this it’s the direction of the velocity of raindrops with respect to the ground.

Here $ {{\overrightarrow{v}} _{rg}}= $ velocity of rain with respect to the ground $ {{\overrightarrow{v}} _{mg}}= $ velocity of the man with respect to the ground.

and $ {{\overrightarrow{v}} _{rm}}= $ velocity of the rain with respect to the man,

We have $ {{\overrightarrow{v}} _{rg}}={{\overrightarrow{v}} _{rm}}+{{\overrightarrow{v}} _{mg}} $ ……(i) T

aking horizontal components equation (i) gives $ {v _{rg}}\sin 30{}^\circ ={v _{mg}}=10km/hr $ or $ {v _{rg}}=\frac{10}{\sin 30{}^\circ }=20km/hr $



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