Question

If the collision is perfectly elastic, what are the final velocities v1 and v2 of objects 1 and 2? give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. express each velocity in terms of v.

Answer 1

. For an elastic head-on (assumed) collision between equal masses, they simply swap velocities. The final velocities of objects 1 and 2 are 0 and v, respectively. 

2. mv = (2m)u 
where u = final velocity. Then u = v1 = v2 = v/2 

3. Initially, p = (2m)v 
final p = 2mv = 2mv1 + mv2 
But for an elastic head-on collision, we know that the 
relative velocity of approach = relative velocity of separation, or 
v = v2 - v1 
v2 = v + v1 
plug into final p: 
2mv = 2mv1 + m(v + v1) = 2mv1 + mv + mv1 
mv = 3mv1 
v1 = v/3 
v2 = v + v/3 = 4v/3 

4. initial p = mv 
final p = mv = (m + 3m)u = 4mu 
u = v1 = v2 = v/4