Question

A ball with a mass of `6 kg` moving at `3 m/s` hits a still ball with a mass of `8 kg`. If the first ball stops moving, how fast is the second ball moving?

Answer 1

Momentum is conserved, so if the first ball stops from the collision, then the second ball will have the same momentum as the first ball did.

Explanation:

The momentum of the firs ball is:

`p = mv`
`p= 6kg * 3m/s`
`p=18 kgm/s`

If that ball stops, then all the momentum is transferred to the second ball,

`p = mv`
`18 kgm/s = 8kgm/s*v`

Solve for `v`

Answer 2

(6 X 3)/8 = 2.25 m per sec in the same direction

Explanation:

Use law of conservation of momentum.
Momentum = mass X Velocity
Ball 1 has mass `m_1` and initial velocity `v_i^1`
Ball 2 has mass `m_2` and initial velocity `v_i^2`
Initial momentum = `m_1` X `v_i^1` + `m_2` X `v_i^2`
Ball 1 has final velocity `v_f^1`
Ball 2 has final velocity `v_f^2`
Final momentum = `m_1` X `v_f^1` + `m_2` X `v_f^2`
Initial momentum = Final momentum
`m_1` X `v_i^1` + `m_2` X `v_i^2 = m_1` X `v_f^1` + `m_2` X `v_f^2`
As initial velocity of Ball 2 is 0 before collision and velocity of Ball 1 is 0 after collision.
`m_1` X `v_i^1` = `m_2` X `v_f^2`