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**Hello forum.**

I have a HW question that I don't fully grasp just yet. It was multiple choice and somehow I guessed the right answer based on the work I did complete, but I want to know how to get to the solution and which steps I'm leaving out. I'll follow the format to write out the question.

1. Homework Statement

I have a HW question that I don't fully grasp just yet. It was multiple choice and somehow I guessed the right answer based on the work I did complete, but I want to know how to get to the solution and which steps I'm leaving out. I'll follow the format to write out the question.

1. Homework Statement

A cannon is mounted on a railway flatcar; both are moving to the right at speed, Vo, relative to the tracks. When the cannon fires a cannonball, the cannon and flatcar recoil so they move to the left at speed, Vo. If M is the total mass of the cannon and railway car without the cannonball, and m is the mass of the cannonball, what is the speed of the cannonball relative to the tracks after it has been fired?

## Homework Equations

Momentum:

p = mv

P (initial) = P(final)

## The Attempt at a Solution

My attempt at a solution started with knowing that momentum would be conserved which meant that p(initial) could be rewritten as M(initial) * V(initial) , and p(final) would be rewritten as M(final) + Vo + m(cannonball) * v(cannonball)

So overall line by line I have:

M(i) * Vo (x^ - unit vector) = M(f)*Vo(-x - unit vector) + m(cannonball) * v(cannonball)

After solving this algebraically, I got the answer for Vo to equal (2*M(i) * Vo / m(cannonball) ), and this answer wasn't listed among the answer choices and the correct answer that I guessed on is not quite this.

I can't seem to find the step that I'm missing.

I also would love if someone could give me a more thorough understanding of what the unit vector notation is, because I keep wanting to think of that x as a variable just from dealing with so much math. But apparently in this instance, it only is an indicator of direction? And it doesn't stand for any value to be solved for?

This is giving me a headache... I appreciate anyone who can help clarify this for me.