Question

A body A, traveling with velocity UA collides perfectly elastically with another body B, initially at rest. (I) if the mass of A is twice that of B, show that, after impact, the velocity VA of A is given as VA=1/3UA

Answer 1

According to momentum conservation:

$$m_Au_A=(m_A+m_B)v_A,\\\space\\ v_A=\frac{m_Au_A}{m_A+m_B}=\frac{2m_Bu_A}{2m_B+m_B}=\frac23 u_A.$$