What is the magnitude of the total momentum of the system that consists of the two balls?

Question

A golf ball with mass 4.500×10−2 is moving in the +x-direction with a speed of 9.45 , and a baseball with mass 0.145 is moving in the -y-direction with a speed of 6.80 .

Answer 1

The magnitude of the total momentum is 1.073794... --- in whatever units you're using (!)

[You didn't SPECIFY any units, but from the order of magnitude of these figures I presume they are kg and m/s. So the units of momentum are' kg m/s.']

This is a simple application of the Pythagorean theorem applied to two PERPENDICULAR components of momentum:

4.500×10−2 (9.45) = 0.42525 in the +x-direction; and
0.145 × 6.80 = 0.986 in the -y-direction.

Then, if the resultant momentum is of magnitude ' R,'

R^2 = (0.42525)^2 + (0.986)^2 = 1.153034..., so that

R = 1.073794... .

QED

For what it's worth, the DIRECTION of the total angular momentum is at an angle of - cos^(-1) (0.42525/1.073794...) = - 66.67... degrees.

Live long and prosper.

Answer 2

Multiply each mass times velocity to get the momentum in the x direction and the momentum in the y direction.

Then, use the pythagorean theorem to get the magnitude. magnitude^2 = is the sum of the squares of the components.

If you need direction (which wasn't asked), use trigonometry. The angle (measured in the usual way counterclockwise from x axis) is the arctangent of the y component over the x.