# a ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to .450 its original speed. what is the mass of the second ball?

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### 1 Answer

You need to use the elastic collision formula, such that:

`m*u + m_2*u_2 = m*v + m_2*v_2`

`m,m_2` represent the masses of the balls

`u,u_2` represent initial velocities, before collision

`v,v_2` represent final velocities, after collision

The initial velocity of the ball `m_2` is `u_2 = 0` and the final velocity of the ball m is ` v = 0.450u` , such that:

`m*u = m*0.450u + m_2*v_2 => mu - m*0.450u = m_2*v_2`

Factoring out `m*u` yields:

`m*u(1 - 0.450) = m_2*v_2 => m_2 = 0.55*m*u/(v_2)`

**Hence, evaluating the mass of the second ball, yields **`m_2 = 0.55*m*u/(v_2).`