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Question

# A man moving at speed of 5 m/s observes rain falling vertically with velocity 5√3 m/s. Find the speed and direction of the rain w.r.t ground.

A
10 m/s, 60 with vertical
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B
10 m/s, 30 with vertical
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C
5 m/s, 60 with vertical
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D
5 m/s, 30 with vertical
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Solution

## The correct option is B 10 m/s, 30∘ with vertical Given, →vr,m=−5√3^j m/s −→vm=5^i m/s →vr,m=→vr−→vm →vr=→vr,m+→vm⇒→vr=(−5√3)^j+5^i m/s |→vr|=√(−5√3)2+52 =√75+25=√100 m/s |→vr|=10 m/s (speed of main w.r.t. ground) Inclination of the rain with vertical, tanθ=55√3=1√3 θ=tan−11√3=30∘ θ=30∘ with vertical

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