Projectile Motion 1 - Measuring the Initial Velocity
First, a couple of resources. Here is some
stuff on kinematics and projectile motion:
Kinematics (constant acceleration)
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
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
Method 2 - Shooting the ball up and measuring the
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
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
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
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
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
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.
Stuff to think about
Which method gave you the best value for the
initial velocity with the smallest uncertainty? Why do you
think this is?