A man moving with velocity 5m/s along a straight line observes rain falling vertically at the rate of 10m/s. Find the speed of rain with respect to ground, and angle(θ) made from vertical by the rain as seen from ground.
A
5√5m/s,θ=tan−142
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B
5√5m/s,θ=tan−112
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C
10m/s,θ=tan−12
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D
10m/s,θ=tan−112
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Solution
The correct option is B5√5m/s,θ=tan−112 Velocity of man with respect to ground →vMG=5^im/s
Velocity of rain with respect to man →vRM=−10^jm/s
Velocity of rain with respect to ground is:
→vRG=→vRM+→vMG
⇒→vRG=−10^j+5^im/s
∴Speed of rain with respect to ground:
|→vRG|=√(−10)2+52=5√5m/s
From the vector triangle, angle made by rain from vertical θ is given as: