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- m(u+v) towards the wall
- m(u+v) away from the wall
- m(u−v) towards the wall
- m(u−v) away from the wall

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Solution

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A ball of mass, m, moving with initial velocity, u to the right towards a wall.

It will have momentum →pi=m→u towards the right.

The ball bounces off the wall. It will now be moving to the left, with the same mass, but a different velocity, v and therefore, a different momentum,→pf=m→v towards the left.

The final momentum vector must be the sum of the initial momentum vector and the change in momentum vector, △→p=m−→△v .

Using tail to head vector addition, △→p, must be the vector that starts at the head of →pi and ends on the head of →pf, hence the resultant change in momentum vector will point towards the left, that is, away from the wall.

We also know from algebraic addition of vectors that:

→pf=→pi+△→p

→pf−→pi=△→p

Direction of change in momentum is towards the left, away from the wall.

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