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[Phys-L] Re: race between car and airplane



John,

An interesting problem. I got the same answers as you (give or take a few 1/10's of a mph for the car). Two notes to add to your notes:

1) Your 3rd assumption is in direct conflict with a section of the problem statement, but since the problem itself is not clear or consistent, that is hard to avoid. (The problem specifically states the car "in still air goes 120 mph", but you are assuming it goes 120 mph with a 20 mph cross-wind as the plane flies above in the same crosswind).

2) Interestingly, after all your analysis of the plane, you get the same result as simple vector analysis. This, of course, is a "Good Thing" since two different solutions to the same problem should give the same answer. It's just a lot easier as a vector addition problem. :-)


Tim Folkerts


-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On Behalf Of John Denker
Sent: Friday, January 27, 2006 11:39 AM
To: PHYS-L@LISTS.NAU.EDU
Subject: race between car and airplane

Here is a problem that might amuse some folks on this list.
Here is the statement of the problem, verbatim as it came to me:

A car on a perfect level surface in still air goes 120 mph using 200 hp. measured at the rear
wheels. An airplane flies directly over the car maintaining exactly the same speed. They both
turn into a 20 mph headwind. What happens? (Give the speeds of both after the turn.) Assume: 1.
The car and the plane apply constant power to the world, before and after the turn. The car’s
transmission has to allow the same power to be developed regardless of speed. 2. The plane files
low so IAS = TAS if that matters. 3. There are no interactions between car and plane. 4. Ignore
turning effects and loss of energy by the plane in the actual turn, we are interested in
steady-state results long after the turn. 5. The car has very very low drag tires so that all the
drag on the car is aerodynamic.

Some remarks:

1) This is intended to represent a real-world problem. There is a
unique, precise, real-world answer.

2) On the other hand, the wording of the statement is IMHO somewhat
obscure if not downright confusing; it may take some effort to figure
out exactly what real-world situation the customer intended to ask about.

Please don't blame me for the wording; this is exactly how the problem
came to me.

There's a lesson in this: I get paid to solve problems like this, and
they almost *never* come to me nicely worded. A huuuge part of the job
is figuring out what the real problem is.

We complain about poorly-worded questions in textbooks, and we agree that
they interfere with learning, especially for beginning students ... but
at some point people need to learn how to handle poorly-worded problems.
Methods for handling such things exist, but IMHO are often not being
taught very well. There is much room for improvement.

3) Beware that even among people who understand the intent of the question,
it is common for them to give a categorically incorrect answer, because
they got the physics completely wrong.

I wrote up my analysis; try solving the problem on your own, then look at:
http://www.av8n.com/physics/car-vs-airplane.htm

4) I can't say much more without giving away the answer ... but I will say
there are some interesting general-purpose lessons that can be drawn from
this, as discussed in the "remarks" section:
http://www.av8n.com/physics/car-vs-airplane.htm#sec-remarks
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