Question

Let me know if you need more information. I need help with the arrows.

Answer 1

The change in momentum is 2 times the length of the momentum vector put in the negative direction.

Step-by-step explanation:

The change in momentum is defined as

`\Delta p=p_f-p_i`

meaning it is the difference between the final and the inital momentum.

Now, our initial momentum is

`p_i=mv_i\vec{i}`

it is in the positive i-direction.

The final momentum is

`p_f=-mv_i\vec{i}`

and it is in the negative i-direction.

Therefore, the change in momentum is

`\Delta p=p_f-p_i=p_f=-mv_i\vec{i}-mv_i\vec{i}`
`\boxed{\Delta p=-2mv_i\vec{i}}`

which is our answer!

Now, what is the direction and magnitude of this momentum vector?

This vector has length 2 and points in the negative i-direction.