Discuss the elastic collision in one dimension and calculate the velocities of bodies after the collision.

Explanation

Consider a body of mass `m_1` moving along x-axis with initial velocity `u_1`. It collides with another body of mass `m_2` at rest.
According to law of conservation of linear momentum
`m_1vecu_1 + 0 = m_1 vecv_1 = m_2vecv_2 `
or `m_1vecu_1 = m_1vecv_1 + m_2vecv_2 " " ....(i)`
The x-component of eqn. (i) gives
`m_1u_1 = m_1v_1 cos theta_1 + m_2v_2 cos theta_2 " " ....(ii)`
and y-component of eqn. (i) gives
`0 =m_1v_1 sin theta - m_2v_2 sin theta_2 " " .....(iii)`
As collision is elastic, so kinetic energy is also conserved
Therefore `1/2 m_1u_1^2 = 1/2 m_1v_1^2 + 1/2 m_2u_2^2" " .....(iv)`
Assume that `m_1, m_2` and `u_1` are known. Now, there are four unknown quantities.
i.e. `v_1, v_2 , theta_1 and theta_2`.
To evaluate these four quantities we need four equations. But we have only three equations i.e. (ii), (iii) and (iv). So, we cannot determine these four quantities. If `theta_1` is also known, then `v_1, v_2 and theta_2` can be calculated.