Predict the landing spot of a ball after a tilted shot

Your job in this exercise is predict where a ball will land when shot from a tilted gun.

Here's the basic setup:

I'll place one of the ballistic pendulum devices on the table at the front of the room. We'll write the values of the heights h1, h2, the angle θ, and the distance from muzzle to front of the table x1 on the board. We'll use the same gun and settings for which we earlier derived the muzzle velocity v. Your job is to predict where the ball will land.

1. Write an equation for finding the time the ball spends in the air. Use symbols for this calculation -- don't put in any numbers yet.
2. Write an equation for finding the distance the ball travels horizontally. Use symbols for this calculation -- don't put in any numbers yet. Your equation should use the time t you found in the previous step.
3. Using the numerical values for height and angle and velocity, predict the distance x2 from the base of the table at which the ball will strike the floor.

How close is your prediction to the actual value?

If you found this exercise interesting, you might consider the associated extra-credit project: estimating the uncertainty in the distance.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.