Question

A ball with a mass of `2 kg` is rolling at `7 m/s` and elastically collides with a resting ball with a mass of `4 kg`. What are the post-collision velocities of the balls?

Answer 1

v1 = -2,33 m/s
v2 = 4,66 m/s

Explanation:

in the elastic collisions remain constant both the total kinetic energy both the momentum. Therefore:
`1/2 m1 v1°^2 = 1/2 m1v1^2 + 1/2 m2 v2^2`.
`m1 v1° = m1 v1 + m2 v2`.
replacing the values in the equation of conservation of momentum, you find:
(1) `v1= 7 -2 v2` .
that you put in the equation of conservation of energy.
Resolving the second degree equation, you find:
`6v2^2 -28 v2 =0`.
then `V2=0` not useful and
`v2 = 4,66 m/s`.
If You put in the (1), you find:
`v1= -2,66 m/s` i.e. the smaller ball comes back.

If you put the values in the equation of conservation of energy, you find that it is verified