# Why does accounting for direction give the wrong result for a bouncing ball?

This a conservation of momentum problem, gathered from an old textbook. I thought it would be simple, but I seem to be goofing up somewhere in my basic conceptual understanding.

PROBLEM: A 1.0 kg steel ball is dropped from 4.0 m above the floor. It strikes the floor and rises to max height of 2.5 m. Find the momentum transferred TO the floor FROM the ball.

My issues: If I tried to solve it using the $y$ axis as a directional path and take vector sign into account, I end up with the wrong answer. However, if I just take into account the magnitude of the steel ball's $p$ immediately before and after the collision I CAN get the right answer. But I cannot reconcile that with my conceptual understanding. Why cannot I get the right answer when I take direction into account?

• Please explain what exactly you have done. How do you solve it? Maybe you have made a mistake in vector calculations. – MEDVIS Nov 28 '14 at 7:45
• I would rather say that this is a conservation of energy problem in disguise ;) Calculate the energy before and after, note that, when the ball is about to strike the ground it will have only kinetic energy, and use the expression for kinetic energy in terms of momentum. Did you do this? – Danu Nov 28 '14 at 8:27
• Kafi - welcome to Physics Stack Exchange! I want to point out that you've done a better job of asking a homework question than many other people, since you quoted your problem, talked about what you tried, and asked about the specific issue that's confusing you. So thanks for that. But it would help us to have some more detail about what exactly you did. Perhaps if you include your actual calculations in the post, someone can identify more specifically what went wrong. – David Z Nov 28 '14 at 9:56

Let's say that the ball strikes the floor with the linear momentum $-p_1$ (you see I take the direction of the momentum in consideration). Some part of the momentum is lost (some energy is lost to the floor) s.t. the ball rises again, but at the floor level it has a linear momentum $+p_2$. So, what the floor "gets" in this scenario? It GETS a linear momentum $+p_1$ and LOOSES a linear momentum $+p_2$. In all, it GETS a linear momentum $-p_1 - p_2$.