### C. __Determination of the Range of the Projectile__

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###### In the above figure, v_{o} = initial velocity of the projectile, h = table
height, R = range of projectile and t_{f} = flight time.

- If the errors in all the other variables are negligible compared to that in v
_{0},
we can ignore the error in h or t_{f} and easily calculate R and its 90%
confidence interval. Do so and check your
results with a neighbor or the instructor.

- This
portion of the lab will be done in the hallway or outside, weather
permitting. Take your apparatus, a meter stick, a piece of carbon paper and
a blank piece of paper to where your instructor has set up the table. In
order to speed things along, make sure you have already calculated your
predicted range to 90% confidence.
- Place the apparatus near the edge of the table. Raise the pendulum until
it latches in the horizontal position.
DO NOT shoot it yet; that would be cheating. Tape one piece of paper with a
piece of
carbon paper on top of it at the position that you think the ball
will hit. Mark the predicted range, R, and its confidence interval on the
paper (extend it out to the sides to account for not being able to line up
the gun perfectly). The carbon paper will record the exact spot where the
ball hits the floor.

- During this portion of the lab, please take special care not to fire
the gun while someone is in the way. Either you or your lab partner should
play the roll of backstop with a wastepaper basket so the projectiles are
not lost. Cock the gun and fire. BE SAFE!

- Fire the gun four more times to see the variations of the range of
each shot. If you are way off, you are going to have to go back and try to
determine what went wrong. If you are off to the side, don't worry since
that is just a question of lining up the gun and marks on the paper.

- Measure the actual range for each shot and calculate an average with a 90% confidence
interval. Compare this to the expected value using the null hypothesis. Make
sure that you have a copy of the marked paper in your notebook.

**If the null hypothesis fails, can you identify some possible sources of
error? Was the random error in the range of the shots the same as the predicted
uncertainty?**