Question

A body of mass m at rest is hit head-on elastically by a body of mass m kg moving with a speed of u.
Find the magnitude and direction of motion of each body after collision.

Answer 1

A body of mass m at rest is hit head-on elastically by a body of mass m moving with a speed of u.

here, $m_1=m_2=m$, $v_1=0,v_2=u$

after head-on collision,

$v_2'=\frac{2m_1v_1}{m_1+m_2}-\frac{m_1-m_2}{m_1+m_2}v_2$

= $\frac{2m\times0}{m+m}-\frac{m-m}{m+m}u$

= 0

$v_1'=\frac{m_1-m_2}{m_1+m_2}v_1+\frac{2m_2v_2}{m_1+m_2}$

= $\frac{m-m}{m+m}\times0+\frac{2mu}{m+m}$

= u

hence, velocity of 2nd body is 0 {i.e., rest} and velocity of first body is u directed in initial velocity of first body.