Question
Starting with equations $m_1v_1 = m_1v_1'\cos(\theta_1) + m_2v_2'\cos(\theta_2)$ and $0 = m_1v_1'\sin(\theta_1) + m_2v_2'\sin(\theta_2)$ for conservation of momentum in the - and -directions and assuming that one object is originally stationary, prove that for an elastic collision of two objects of equal masses, $\dfrac{1}{2}mv_1^2 = \dfrac{1}{2}mv_1'^2 + \dfrac{1}{2}mv_2'^2 + mv_1'v_2'\cos(\theta_1 - \theta_2)$ as discussed in the text.

see video for derivation.

Solution Video