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Re: Relative velocity problem....



Please help me get a concept across to my students. Here is the problem:

A person rides in the back of a pick-up truck moving forward at +20 mph
(relative to ground). The person throws a brick toward the back of the
truck at -5 mph (relative to the truck). What is the resultant velocity of
the brick relatvive to the ground?

I know that the brick will move forward at + 15 mph relative to the ground.
My students can't really believe this. Oh, they will accept it simply
because I told them that is what happens, but they do not really believe
that you can throw something backwards yet have it really be moving
foreward relative to the ground. I have no modeling software (i.e.
Interactive Physics) at the moment. And short of going to the parking lot
with a truck and a brick (maybe basketball -- safer) I am at a loss getting
them to believe this.

They accept that if they throw the brick backwards at -20 mph the brick
will have no velocity relative to the ground and will simply fall. And
they accept that if they throw the brick straight up it will land back in
the truck (after some simple demos). Yet they will not accept the brick
moving forward. I know, I know.... if they accept the others, it is a
logical conclusion. But they don't see it.

Any ideas?

Ralph von Philp
Boonsboro High School, MD

I don't know what time frame you are constrained by, but Pasco has a new
version of the old vertically fired mortar on a cart (a first law
demonstrator). This one can be tilted, so that the ball is fired at an
angle to the vertical. Try tilting the mortar backwards a bit, so that when
the cart held at rest, the ball travels toward the back of the cart and
doesn't come back down in the hole. Then launch the cart to the right (say)
and have the students note where on the track the ball is launched, and
where it lands. If you choose the angle right, the ball should land ahead
of the launch point, even though it was fired aiming "backwards."

Caveat: I haven't tried this myself. Our Pasco mortar is presently out of
commission for lack of some essential parts. Try it yourself in private
before demonstrating it to your students. It seems to me that it should
work, but I don't have a feel for how difficult it will be for the students
to tell where the launch point is relative to the landing point.

Failing this, I guess I would try to see if the students will accept that a
ball dropped by a passenger in a uniformaly moving car will land at the
passenger's feet. Most should accept this. If not have them try it as a
homework assignment. Then ask them where a ball tossed backwards will land
relative to the release point (relative to the person tossing the ball).
Then calculate where the landing point is relative to the ground. If the
ball lands ahead of the point on the ground where it would have had the car
been at rest, that should convince some of them.

As I write this, I am thinking that maybe the problem is with the "open"
bed of the truck. Because of the obvious air resistance in the truck bed,
the ball will quickly assume the speed of the air, and will behave much
more like the students believe that like we would like them to. Have them
redo the problem inside a closed vehicle (an airliner is a good example,
because of its great speed relative to the gorund).

Your suggestion of taking them outside and showing them what happens is
probably the best. If you have any football players in your class, have
them demonstrate by having one of them toss a "lateral" to a trailing
player as they both run past a given point on the field, and then see that
the trailing player catches the ball farther up field than it was thrown,
even though it was thrown "backwards."

These are all pretty obvious solutions, but this is a real problem for some
students. Relative velocity is not an easy concept to grasp, and good ways
of demonstrating it are not easy to come by. I would be interested in
hearing how you solve the problem. Good luck.

Hugh

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Hugh Haskell
<mailto://hhaskell@mindspring.com>
<mailto://haskell@odie.ncssm.edu>

Instructor of Physics, NC School of Science and Mathematics
P. O. Box 2418, Durham, NC 27715
(919) 286-3366

The box said "Requires Windows 95 or better." So I bought a Macintosh.
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