AP Physics

The Raindrop Problem

The Situation:

Rain and car diagramAs 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:

vr = the terminal velocity of the raindrops, and

vc = 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 vr in terms of vc 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 55o to the horizontal, what is the terminal velocity of a raindrop?

Hints & Suggestions:


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

copyright 1997, 1998 by Jerry L. Stanbrough - all rights reserved
last update January 14, 1998 by JL Stanbrough ( jstanbro@venus.net)