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The problem is a one-dimensional perfectly-inelastic "dead-on"
collision. Mass one (m1) comes in with initial velocity v1i and
strikes stationary mass two (m2). The two masses stick together
and the combined mass (m1+m2) goes off with final velocity vf.
The data for the problem are m1, m2, and v1i and a statement that
the collision is perfectly inelastic. Part-A of the problem asks
them to solve for vf. Part-B of the problem asks them to solve
for the percentage of KE retained.
I assumed students would get the percentage by KEf/KEi*100%.
However, one student got the correct answer by vf/v1i*100%. I
first marked it wrong with the comment that the answer was
accidentally correct. But then I did a little algebra and
discovered this method is correct in general.
I still think the student made a lucky guess,
I doubt the
student knew that. I've never seen it before. Has anybody on
the list seen this? Does this appear in any textbook you are
aware of?