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A man running on a horizontal road at 8km/h finds the rain falling vertically. He increases his speed to 12km/h and finds that the drops make angle 30 degree with the vertical. Find the speed and direction of rain with respect to the road. Please help me out in making a diagram for this one. Thanks.

A man running on a horizontal road at 8km/h finds the rain falling vertically. He increases his speed to 12km/h and finds that the drops make angle 30 degree with the vertical. Find the speed and direction of rain with respect to the road.
 
Please help me out in making a diagram for this one.
 
Thanks.

Grade:11

3 Answers

ADITI SINGH
95 Points
7 years ago
Since when the person runs at 8 km/h the rain seems to be coming verticaly down thus the horizontal component of rain, Vx is 8 km/h
When he incrreases his relative speed by 4 km/h with the horizontal component of rain, it seems to fall at an angle of 30 degrees with the vertical.
It means the vertical component, Vy is: 4/Vy = tan 30
i.e.
Vy = 6.93 km/h
V = 10.58 km/h
and angle of falling is: tan-1(8/6.93)
Shyam Ardeshna
11 Points
6 years ago
When the man runs at 8 km/hr ☔️ rain falling along y axis and when he runs at 12 km/hr the angle with y axis is 30 degrees 
So by relative velocity we can stop the man in case 1 and decrease the speed in case 2 by 8km/hr.
So now relative speed is 4 km/hr along horizontal and angle with vertical is 30 degrees.
 
Tan 30 = x/4
Calculate (x) which is speed of rain wrt ground
Answer is 4*root3
 
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

This shows that the horizontal component of rain =8 km/hr
as the relative velocity of the rain has only a vertical component with respect the man.
Vx​=8 km/hr
2nd case →VRM​=VR​−VM​=(8↑−Vy​↑)−12↑=−4↑−Vy​↑
tan30o = 4/Vy​
⇒ ​1/root(3) ​= 4/Vy​​
Vy​ = 4root(3)​ km/hr
⇒∣V∣ =4root(3) km/hr
Velocity of Rain = 8 km/hr↑−4root(3)​ km/hr↑
⇒ tanα = ​2/root(3)​ from vertical

Thanks and Regards

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