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A man running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops make angle `30^0` with the vertical. Find the speed and direction o the rain with respect to the road.

Text Solution

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Let the speed of rain with respect to the road is v and the angle formed by rain with vertical is 0.

For the first case
8 = v sin 0.......(i)
For the second case
`12 = v sin 0 +u sin 30^(@)........(ii)`
and `u cos 30^(@) =v cos 0........(iii)`
From (i) and (ii)
`12=8 + u sin 30^(@) rarr u =8 km//h.....(iv)`
From (iii) and (iv) `v cos 0 =sqrt(3)`
`? v^(2)=8^(2) +(4 sqrt(3))^(2) rarr v=4 sqrt(7) km//h`
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