Question

Question #83c7e

Answer 1

I found that depends on the ratio of the two masses only.

Explanation:

I tried considerng Conservation of Momentum `p` (along `x`):
Before: `0`
After: `m_1v_1+m_2v_2`
and together:
`0=m_1v_1+m_2v_2`

so: `m_1v_1=-m_2v_2`

squaring both and rearranging:

`v_1^2/v_2^2=m_2^2/m_1^2`

Kinetic Energy is `K=1/2mv^2`
So:
`K_1/K_2=(cancel(1/2)m_1v_1^2)/(cancel(1/2)m_2v_2^2)`,
substituting: `v_1^2/v_2^2=m_2^2/m_1^2`
`K_1/K_2=(cancel(m_1))/(cancel(m_2))*m_2^cancel(2)/m_1^cancel(2)=m_2/m_1`