### C. Determination of the Range of the Projectile

###### In the above figure, vo = initial velocity of the projectile, h = table height, R = range of projectile and tf = flight time.
1. If the errors in all the other variables are negligible compared to that in v0, we can ignore the error in h or tf and easily calculate R and its 90% confidence interval. Do so and check your results with a neighbor or the instructor.
2. 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.
3. 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.
4. 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!
5. 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.
6. 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?