How Does Wall Impact Affect Momentum and Force Calculation?

[j_namtirach]

Hello,

This is an IB question:

Homework Statement

A sphere of mass m strikes a vertical wall at right angles and bounces off it.

The magnitude of the momentum of the sphere just before impact is pB and just after impact is pA. The sphere is in contact with the wall for time t. The magnitude of the average force exerted by the wall on the sphere is:

A. (pB - pA)/t
B. (pB + pA)/t

Homework Equations

F = Δρ/t

The Attempt at a Solution

My friend and I have a disagreement about which of the two answers is correct and why. I believe that the answer should be A, as momentum is a vector. My friend thinks it should be B as he says there is no direction given for the momentum. My thinking is that momentum is a vector and the direction actually is given in the question anyway. Can anyone explain which one is the correct answer and why? Any answers would be greatly appreciated.

Thanks

 

[voko]

The problem explicitly said that both values given are the magnitudes.

Now that you know the directions, can you restore the vectorial values of the momenta?

 

[j_namtirach]

The question actually has a diagram which I couldn't include. On the diagram, pB has a direction towards the wall and pA has a direction away from the wall. This suggests to me that the direction is given. Am I missing something?

 

[voko]

pB and pA are said to magnitudes; they cannot have directions.

Direction is a property of a vector. In #2, I asked you whether with the information you are given you can restore the vectors.

 

[haruspex]

The question actually has a diagram which I couldn't include. On the diagram, pB has a direction towards the wall and pA has a direction away from the wall. This suggests to me that the direction is given. Am I missing something?

The momentum is a vector and so has direction. The diagram is telling you the magnitude (pA) and the direction (the arrow) separately. It does not turn 'pA' into a vector.