The uncertainty in a projectile's distance

In class, we did an activity in which you predicted where a ball would land when shot from a tilted gun.

Here's the basic setup:

Given the values for variables

• heights h1, h2
• angle θ
• distance from muzzle to table x1
• muzzle velocity v

one can calculate how far the ball will travel before striking the floor; and, therefore, the distance x2 from the landing spot to the base of the table.

But what if each of the five quantities has an uncertainty? That must mean that the predicted landing spot is also uncertain. How large will the uncertainty in its location be?

Your job: use any method of your choice to estimate this uncertainty. Given these values:

• h1 = 81.0 +/- 1.0 cm
• h2 = 13.0 +/- 0.5 cm
• x1 = 7.0 +/- 0.5 cm
• v = 363.0 +/- 8.0 cm/s
• θ = 23.0 +/- 2.0 degrees

What is the value of the horizontal distance x2? What is its uncertainty?

Write a brief report showing all your work, and submit a hardcopy to the instructor.

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