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 $
BETA
