Question

two balls of masses m and 2m moving in opposite direction collides head on elastically with velocity v and 2v . find their velocities after collision

Answer 1

mass of 1st ball , $m_1$ = m
mass of 2nd ball, $m_2$ = 2m
initial velocity of 1st ball , $u_1$ = -v
initial velocity of 2nd ball, $u_2$ = 2v

use law of conservation of linear momentum,
$m_1u_1+m_2u_2=m_1v_1+m_2v_2$
$-mv+4mv=m(v_1+2v_2)$
$3v=v_1+2v_2$......(1)

use law of conservation of energy,
$\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2$
$mv^2+(2m)(2v)^2=m(v_1^2+2v_2^2)$

$9v^2=v_1^2+2v_2^2$.....(2),

from equations (1) and (2),
$v_1=-v$ and $v_2=2v$