Predict the landing spot of a ball
Your job in this exercise is to watch very carefully as a
ball is shot out of a gun, flies through the air,
and lands on the floor.
After you have analyzed its motion, you must predict where
the ball will land when shot from a slightly different location.
Here's the basic setup:
I'll place one of the ballistic pendulum devices on
the table at the front of the room.
We'll write the values of the heights
on the board, then fire gun.
I'll measure the distances x1, x2
and write those on the board, too.
- Determine the uncertainty in the total height
and total horizontal distance.
- Calculate the initial speed v of the ball when it
leaves the muzzle of the device.
Explain to me in writing your method, and show all
- Determine the uncertainty in v.
- Write an equation which describes the range of the ball
when fired from any height H.
So, for example, if I placed your gun 2 meters above the floor,
or 5 meters, or 10 meters, how far would the ball go?
- Predict the distance the ball will travel if shot from
one of the student tables.
I'll measure the height of the table -- ask me for the
value and its uncertainty.
You must show me or the assistant your result before
you can continue!
If you want full credit, you'll again have to deal with uncertainties,
and end up by showing me a range: "the ball will travel
156 +/- 3 cm", or something like that.
Near the end of the class, I'll move the gun to one of the
student tables and fire it.
Your score will depend on how well your prediction
and its uncertainty matches the actual distance.
How do you deal with combining two measurements, each of which
has an associated uncertainty?