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Question

A man moving with velocity 5 m/s along a straight line observes rain falling vertically at the rate of 10 m/s. Find the speed of rain with respect to ground, and angle(θ) made from vertical by the rain as seen from ground.

A
55 m/s, θ=tan142
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B
55 m/s, θ=tan112
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C
10 m/s, θ=tan12
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D
10 m/s, θ=tan112
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Solution

The correct option is B 55 m/s, θ=tan112
Velocity of man with respect to ground
vMG=5^i m/s

Velocity of rain with respect to man
vRM=10^j m/s

Velocity of rain with respect to ground is:

vRG=vRM+vMG

vRG=10^j+ 5^i m/s

Speed of rain with respect to ground:

|vRG|=(10)2+52=55 m/s

From the vector triangle, angle made by rain from vertical θ is given as:


tanθ=|vMG||vRM|

tanθ=510=12

θ=tan112

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