In response to Michael's question about the student who answered the
question about the percent KE retained by using vf/v1i, this is something
I show my intro. physics students at least twice.
In analyzing a ballistic pendulum, for instance, you get this result. I
derive it by saying:
KE initial = 0.5 m v1i^2 = 0.5 (m v1i) v1i
KE final = 0.5 M vf^2 = 0.5 (M vf) vf
The 0.5's cancel, and then the terms in brackets cancel - conservation of
linear momentum - which quickly leads to exactly what the student got:
KEf/KEi = vf/v1i
I do a similar thing later in the semester in analyzing the rotational KE
of a figure skater who pulls her arms in, to show that the rotational KE
goes up when she does this.
As for where the student got it from, that's a good question. It would be
interesting to ask the student and see what he says.