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

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

Grade:11

1 Answers

Harshit Singh
askIITians Faculty 5965 Points
11 months ago
Dear Student

This shows that the horizontal component of rain=8km/hras the relative velocity of the rain has only a vertical component with respect the man.
Vx​=8km/hr
2ndcase
→VRM​=VR​−VM​
=(8↑−Vy​↑)−12↑
=−4↑−Vy​↑
tan30o= 4​ /Vy
⇒ 1​ / √3 = 4​ /Vy​
Vy​ = 4√3​km/hr

Velocity of Rain= 8km/hr↑−4√3​km/hr↑
⇒tan α = ​2​ / √3 from vertical.


Thanks

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