I already have the answer, I just need someone to help me understand the answer for the following momentum question:
Two balls are both moving horizontally to the right on a table. Ball 1 catches up with ball 2 and collides with it. The balls stick together and continue on with velocity vf (balls are still moving horizontally and are still on the table). Which of these statements is true?
a) vf is greater than v1.
b) vf = v1.
c) vf is greater than v2 but less than v1.
d) vf = v2.
e) vf is less than v2.
f) Can't tell without knowing the masses.
The ANSWER is c.
the law of conservation of momentum: vector Pf = vector pi
The Attempt at a Solution
THE CORRECT ANSWER:
Momentum conservation requires (m1 + m2) * vf = m1v1 +m2v2. Because v1>v2, it must be that (m1 +m2) * vf = m1v1 + m2v2 > m1v2 +m2v2 = (m1 + m2) * v2. Thus vf > v2. Similarly, v2 < v1 so (m1 + m2) * vf = m1v1 + m2v2 < m1v1 + m2v1 = (m1 + m2) * v1. Thus vf < v1. The collision causes m1 to slow down and m2 to speed up.
I got this answer from the back of my physics textbook so I am 100% sure it is CORRECT. Right now, I am studying for my midterm on Friday, and I would REALLY appreciate it if someone could explain the answer to me!