# AP Physics

# The Raindrop Problem

##

The Situation:

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

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