Aspring is compressed between two cars on a frictionless airtrack. car a has four times the mass of car b, ma = 4 mb, while the spring’s mass is negligible. both cars are initially at rest.
when the spring is released, it pushes them away from each other.

which of the following statements correctly describes the velocities, the momenta, and the kinetic energies of the two cars after the spring is released?

note: velocities and momenta are given below as vectors.

1. ~va = −~vb ~pa = −4~pb ka = 16 kb

2. ~va = + 1 5 ~vb ~pa = + 4 5 ~pb ka = 4 25 kb

3. ~va = + 1 4 ~vb ~pa = +~pb ka = 4 kb

4. ~va = − 1 4 ~vb ~pa = −~pb ka = 1 4 kb

5. ~va = −2~vb ~pa = −8~pb ka = 16 kb

6. ~va = −~vb ~pa = −~pb ka = kb

7. ~va = − 1 3 ~vb ~pa = − 2 3 ~pb ka = 4 3 kb

8. ~va = − 1 2 ~vb ~pa = −2~pb ka = kb

9. ~va = −4~vb ~pa = −16~pb ka = 64 kb

10. ~va = − 1 4 ~vb ~pa = −~pb ka = 4 kb