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Question

A man running on a horizontal road at 8 ms1 finds rain falling vertically. If he increases his speed to 12 ms1, he finds that drops make 30 angle with the vertical. Find the velocity of rain with respect to the road.

A
47 ms1
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B
82 ms1
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C
73 ms1
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D
8 ms1
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Solution

The correct option is A 47 ms1
Let velocity of rain Vr=Vrx^i+Vry^j
Velocity of rain wrt man,
Vrm=(VrxVm)^i+Vry^j

case (i)
VrxVm=0vrx=8 ms1
case (ii)
tan30=VrxVmVry=812Vry
Vry=43 ms1

Vr=8^i43^j=422+3=47 ms1

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