AP Physics

The Raindrop Problem

The Situation:

Rain and car diagram As a passenger in a car on a rainy day, I noticed that, above a certain speed, no raindrops landed on the rear window. It occurred to me that knowing the speed of the car and the angle of the rear window, one could calculate the terminal velocity of the raindrops!

The Problem:

It was a calm day (no wind), so the raindrops were falling straight down relative to the Earth. Since the raindrops had been falling for a long time (relatively speaking), it would be reasonable to assume that they had reached their terminal velocity and were falling at constant speed.

(a) If:

v_r = the terminal velocity of the raindrops, and
v_c = the minimum speed of the car at which raindrops don't land on the rear window, and

q = the angle that the rear window makes with the horizontal,

derive an expression for v_r in terms of v_c and q.

(b) If the car's speedometer reads 100 km/hr when no raindrops hit the rear window, and the car's rear window makes an angle of 55^o to the horizontal, what is the terminal velocity of a raindrop?

Hints & Suggestions:

Keep in mind that both the car and the raindrops are moving at constant velocity,although at right angles to each other.
If you have trouble analyzing the problem in the Earth frame of reference, you can always consider the motion of the raindrops relative to the car.
Simplifying the problem sometimes helps - there are certain window angles that make the relationship between the speeds very easy...
This problem should be easy to simulate using "Interactive Physics" . This could provide some "experimental data" to check your analysis...
DO NOT try to study the rain falling on the rear window of a car WHILE YOU ARE DRIVING the car!!

References:

This problem is adapted from Pietro Ferraro, "Raindrops Keep Falling on My Car, but Not on the Rear Window", in The Physics Teacher, Vol. 35, Dec. 1997,p. 523-524, AAPT

last update January 14, 1998 by JL Stanbrough ( jstanbro@venus.net)