Do you remember that episode of Mythbusters where the build team wanted to test whether or not firing an object backwards with a certain velocity while going forwards with the same velocity would cancel out the momentum?
In it, they went through dozens of tests, trying to get the air cannon to fire with exactly the right velocity and finally they got it so it canceled out just perfectly and the ball dropped straight down?
Very cool demonstration except for one thing: Doing dozens of tests and then picking the one you want to be right doesn't actually tell you anything. What would really be necessary is seeing if the average actually comes out to be zero.
This would require getting all the high speed footage from all the tests, analyzing it, finding the average, and standard deviation (which is related to the experimental uncertainty) to see whether or not the average truly fell where it should. Quite a bit of work, but I bet students would love it.
Topics it would address:
Velocity and/or momentum as vectors