How Does Relative Motion Affect Raindrop Trajectories on a Moving Car?

[AdnamaLeigh]

A car travels east with a horizontal speed of 51.1km/h. Rain is falling vertically with respect to Earth. The traces of the rain on the side windows of the car make an angle of 61.2 degrees with the vertical.
Find the magnitude of the velocity of the rain with respect to the car.
Find the magnitude of the velocity of the rain with respect to Earth.

How can the magnitudes be different? I don't even know how to illustrate this.

 

[BobG]

The magnitudes have to be different. The rain is falling straight down at some velocity - that's the magnitude of the velocity relative to the Earth.

To get the velocity relative to the car, you have to add in the car's velocity. Keep in mind that the car is traveling perpendicular to the rain, so the easy way to get the magnitude of the two added together will be the Pythagorean theorem.

Draw a triangle. You have the horizontal component. You have the angle opposite the horizontal component. You also know the rain's velocity and the car's velocity are perpendicular, giving you a right triangle.

With a little trig, you can figure out both the hypotenuse and the vertical component. (The hypotenuse will be the velocity of the rain relative to the car).

 

[andrevdh]

Well, firstly consider what it would look like when observing a single drop of rain falling while traveling in a moving vehicle. As the drop falls a bit downwards you move a bit forward. Therefore it will appear to you that the drop is falling at an angle slanted backwards from the vertical. You would therefore conclude that it is moving not vertically downwards, but at some angle w.r.t. the vertical. The more so the faster you are travelling. The drop moving in the opposite direction with the same speed as you therefore would explain it's motion as viewed by you. This information should enable you to construct the vector triangle and solve it (it is a simple matter of x- and y components of a vector with the magnitude and angle given). If not, you will need to consult your handbook on how to add relative velocities up.

 

[borisleprof]

Trace a right triangle with a horizontal side = 51.1 an vertical side = v (the speed of the rain. Now Now in your figure, 51.1/v = tan 61.2; so v=51.1/tan61.2 ≈ 28.

So the sped of the rain directly on the Earth is around 28 km/h.

But as seen by the driver, rain do not falls verticaly but along the hytenuse of the right triangle. this hypotenuse measure √(51^2 +28^2) ≈58.3 km/h.