Question

A person looking out of the stationary train notices the raindrops falling vertically downward at a speed 5 m/s relative to the ground. When the train moves at a constant velocity, the raindrops make an angle of 45* when they move past the window with the vertical. How fast is the train moving ?

Please explain with a proper diagram

Answer 1

Answer

Correct option is

A

4 m/s

The velocity of rain with respect to the man=4m/s at an angle 30° with vertical.

Also, it is given that the velocity of the man with respect to ground=4m/s

The velocity of rain wrt man+velocity of man wrt ground = velocity of rain wrt ground i.e actual velocity of the rain

(by using and applying triangle law of vector addition)

So, velocity of rain wrt ground=

4

2

+4

2

+2(4)(4)cos120

=

16+16+32(−0.5)

=

32−16

=

1

6

=4m/s

Therefore the actual velocity of the rain with respect to ground=4m/s