A ball of mass m1 moves at speed v1 along the positive x-axis toward a second ball of mass m2, which is initially at rest. The second ball has 8 times the mass of the first ball. After the collision between these two objects, m1 moves along the positive y-axis at a speed v1, and m2 moves at a speed v2 = (1/4)v1 at an angle of 31.2° below the positive x-axis.

a) Find the momentum change of the ball of mass m1 during the collision. Give your answer in x- and y-component form; express the components in terms of m1 and v1.

Lets draw a "before" and "after" picture.

Before:
screenshot_10
After:
screenshot_12

Now that we have the correct picture, lets write down the momentum principle for mass 1:
screenshot_13
Where F1 is the force mass 2 exerts on mass 1.
And here is the momentum principle for mass 2:
screenshot_14

During this collision, Newton's third law still works, so
screenshot_15
Rewriting the momentum principle for mass 2:
screenshot_16
And so:
screenshot_17

Which says that the changes in momentum for the two objects are equal, but opposite.

So, to find the change in momentum for mass 1, we can find the change in momentum for mass 2. Mass 2 was initially at rest, so its final momentum is the same as the change in momentum. But it is a vector, so (for the numbers provided above):screenshot_18
Replacing m2 with 8m1 and simplifying:


screenshot_19