Projectile Motion 1 - Measuring the Initial Velocity

First, a couple of resources. Here is some stuff on kinematics and projectile motion:

Kinematics (constant acceleration)

Projectile Motion

Now for the objective:

The main goal of this lab is to determine the launch velocity of a ball launcher with uncertainty. You are going to do this three different ways for the lowest launch setting. (make sure you always use the same mass ball. If you like, you can try changing the mass of the ball and seeing what happens). You will certainly need to recall the stuff about propagation of error.

Method 1 - Shooting the ball up and using a stop watch

Point the launcher straight up. Shoot the ball. Measure the time (with a stop watch) for the ball to go up and back down. Ideally, it should land right back in the launcher, but I doubt that will happen. Do this several times so that you can get an uncertainty in the time measurement (like 5 times). This would be much better than estimating the uncertainty from one single measurement.

Can you calculate the launch velocity from the average time? (you should be able to). Calculate the uncertainty in the launch velocity also. You can assume g = 9.8 m/s^2 with no uncertainty.

Method 2 - Shooting the ball up and measuring the maximum height

Once again point the launcher straight up. Shoot the ball. This time try to measure how high the ball travels before moving back down. To get a more unbiased measurement, let other group members measure this height. Repeat several times to get the uncertainty. Use this to calculate the initial velocity of the ball.

Method 3 - Shoot the ball horizontally off the table.

For this method, aim the launcher horizontally to shoot the ball on to the floor. Use carbon paper and normal paper to mark the location on the floor where the ball lands. Use the stop watch to measure how long the ball is in the air.

Since there is no acceleration in the horizontal direction, you can calculate the horizontal velocity using the measured distance and time. Repeat several times to get an uncertainty in both horizontal distance and time. Calculate the uncertainty in the launch velocity.

Method 4 - Shoot the ball horizontally off the table again.

This time, measure the horizontal distance in the same manner is method 3. Measure the initial height of the ball above the ground. Repeat several times to get an uncertainty in both height and horizontal distance. You might want to just estimate the uncertainty in the height since you would probably get the exact same measurement each time.

To calculate the initial velocity, first JUST look at the vertical motion. Use the kinematic equations to determine the time. Then use this time in the horizontal motion. Again, calculate the uncertainty in the velocity.

Here is some more stuff on projectile motion.

Other Methods

Can you think of any other ways to measure the initial velocity of the ball? Try it if you can and determine the uncertainty in the initial velocity.