Physics Question on work, energy and power

Question

A ball moving with velocity $2\, m/s$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$ , then their velocities $(in\, m/s)$ after collision will be

Answer 1

Solution

Here, m $_1$ = w, m $_2$ = 2m
u $_1$ = 2 m/s, u $_2$ = 0
Coefficient of restitution, e = 0.5
Let v $_1$ and v $_2$ be their respective velocities after collision.
Applying the law of conservation of linear momentum, we get
$m_1u_1+m_2u_2=m_1v_1+m_2v_2$
$\therefore m \times 2 +2m \, \, \times \, 0 = m\times v_1 +2m \times v_2$
or $2m = mv_1 + 2mv_2$
or 2 = ( $v_1$ + 2 $v_2)$ ...(i)
By definition of coefficient of restitution,
$e=\frac{v_2 -v_1}{u_1 -u_2}$
or $e(u_1 -u_2)=v_2-v_1$
0.5(2 - 0) = $v_2 - v_1$ ...(ii)
$1=v_2-v_1$
Solving equations (i) and (ii), we get
$v_1 = 0\, m/s$ , $v_2 = 1\, m/s$