An 14g object moving to the right at 32cm/s overtakes and collides elastically with a 34g object?

Question

Moving in the same direction at 20 cm/s. Find the velocity of the object which is slower after the collision. Answer in units of cm/s.

Answer 1

We assume a head-on collision.
Notation is: V = velocity, M = mass, CR = coefficient of restitution (=1 when elastic), KE = kinetic energy; 1, 2, CM, Rel = body 1, body 2, system, relative (body 1 relative to body 2); (i), (f) = initial, final.
M1,M2 = .014 .034
V1(i),V2(i) = .32 .2
VCM = (M1V1(i)+M2V2(i))/(M1+M2) = .235
VRel(i) = V1(i)-V2(i) = .12
VRel(f) = -CR*VRel(i) =-.12
V1(f) = VCM+VRel(f)*M2/(M1+M2) = .15
V2(f) = VCM-VRel(f)*M1/(M1+M2) = .27
KE1(f) = M1*V1(f)^2/2 = .0001575
KE2(f) = M2*V2(f)^2/2 = .0012393
The answer to the question is V1(f) and is in m/s. Note that in a head-on elastic collision the initially faster object is always finally slower.
The ref. explains in more detail and provides a calculator where you can verify these results.