If the magnitude of the initial velocity of the ball v0 = 7.94 ± 0.03, and the "gun" is tilted 31 ± 0.4º upwards, what is the uncertainty in the horizontal component of velocity σvx?

0.05

Explanation:

Given a variable C which is the product of two variables A, B:

Then the absolute error on C is given by:

where are the uncertanties on the measure of A, B and C, respectively.

In this problem, the horizontal component of the velocity is given by

Therefore, the uncertainty on vx is given by:

(1)

where we have:

, so

The uncertainty on is given by:

where:

and

So

Also,

So, combininb everything into (1), we find: