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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 300 to the vertical.Find the actual velocity of the rain.

Eshan
2 years ago
Let the drop fall at angleand speed. Let the speed o man be. Since the rain appears to fall vertically,$\dpi{80} u=vsin\theta$

When the man doubles the speed, the relative speed of rain backwards=$\dpi{80} 2u-vsin\theta$
The relative speed of rain vertically downward=

Since it forms anglewith vertical. Hence$\dpi{80} tan30^{\circ}=\dfrac{2u-vsin\theta}{vcos\theta}$

Solving the two gives the value of v.
Eshan
The answer comes out to be$\dpi{80} v=4km/hr$and$\dpi{80} \theta=30^{\circ}$