# Classic rain falling on a car's window problem doubt

A car travels due east with a speed of 50.0 km/h. Raindrops are falling at a
constant speed vertically with respect to the Earth. The traces of the rain on the
side windows of the car make an angle of 60.0° with the vertical. Find the
velocity of the rain with respect to (a) the car and (b) the Earth.

I got the right answer, I considered in (a) the x-component of v(rain) the same as the horizontal component of the car's velocity, and the by trigonometry calculated the y-component.

However, I have a doubt: If the rain has only vertical velocity relative to the car, why do the traces make an angle of 60º with the vertical? For me that must mean the rain has displacement relative to the car and thus the horizontal component of the rain's velocity relative to the car is not zero!

Could you clarify this to me?

## Answers and Replies

gneill
Mentor
A car travels due east with a speed of 50.0 km/h. Raindrops are falling at a
constant speed vertically with respect to the Earth. The traces of the rain on the
side windows of the car make an angle of 60.0° with the vertical. Find the
velocity of the rain with respect to (a) the car and (b) the Earth.

I got the right answer, I considered in (a) the x-component of v(rain) the same as the horizontal component of the car's velocity, and the by trigonometry calculated the y-component.

However, I have a doubt: If the rain has only vertical velocity relative to the car, why do the traces make an angle of 60º with the vertical? For me that must mean the rain has displacement relative to the car and thus the horizontal component of the rain's velocity relative to the car is not zero!

Could you clarify this to me?

The answer to your question is in the problem statement: "Raindrops are falling at a
constant speed vertically with respect to the Earth" (emphasis added).

jfizzix
Science Advisor
Gold Member
The rain down not have only a vertical velocity relative to the car.

If you consider the Earth as a stationary frame of reference, the Earth has velocity zero, and the rain has only a vertical component of velocity. Assuming a level road, the car has only a horizontal component of velocity.

To go to the reference frame of the car, subtract the velocities of everything by the velocity of the car.

Then, in the car's reference frame, its own velocity is zero, the Earth's velocity is horizontal and in the backwards direction, and the velocity of the rain would have a vertical and horizontal component as you say.