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To a man walking at the rate of 2km/hr, rain appears to fall vertically.When he doubles his speed,it appears to fall at 30 0 to the vertical.Find the actual velocity of the rain.

To a man walking at the rate of 2km/hr, rain appears to fall vertically.When he doubles his speed,it appears to fall at 300 to the vertical.Find the actual velocity of the rain.

Grade:12th pass

2 Answers

Eshan
askIITians Faculty 2095 Points
2 years ago
Let the drop fall at angle\thetaand speedv. Let the speed o man beu. Since the rain appears to fall vertically,u=vsin\theta

When the man doubles the speed, the relative speed of rain backwards=2u-vsin\theta
The relative speed of rain vertically downward=vcos\theta

Since it forms angle30^{\circ}with vertical. Hencetan30^{\circ}=\dfrac{2u-vsin\theta}{vcos\theta}

Solving the two gives the value of v.
Eshan
askIITians Faculty 2095 Points
2 years ago
The answer comes out to bev=4km/hrand\theta=30^{\circ}

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