Vectors Question 177
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
Correct Answer: B 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. 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}} _{r,m}}+{{\overrightarrow{,v}} _{mg}} $ ……(i) Taking horizontal components equation (i) gives $ {v _{r,g}}\sin ,30{}^\circ ={v _{m,g}}=10,km/hr $ or $ {v _{r,g}}=\frac{10}{\sin 30{}^\circ }=20,km/hr $Show Answer
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BETA
