Question

A ball with a mass of `8 kg` moving at `3 m/s` hits a still ball with a mass of `15 kg`. If the first ball stops moving, how fast is the second ball moving?

Answer 1

`1.6\ \text{ m/s}`

Explanation:

The linear momentum in a collision always remains conserved irrespective of type of collision elastic or inelastic.

If `v_1=0` & `v_2` are the velocities of balls of masses `m_1=8\ kg` & `m_2=15\ kg` moving with initial velocities `u_1=3\ m/s` & `u_2=0` respectively, after collision then

by the conservation of linear momentum, we have

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

`8(3)+15(0)=8(0)+15v_2`

`24=15v_2`

`v_2=24/15`

`v_2=1.6\ \text{ m/s}`

hence, the velocity of second ball, after collision, is `1.6` m/s

Answer 2

The velocity of the second ball after the collision is `=1.6ms^-1`

Explanation:

We have conservation of momentum

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

The mass the first ball is `m_1=8kg`

The velocity of the first ball before the collision is `u_1=3ms^-1`

The mass of the second ball is `m_2=15kg`

The velocity of the second ball before the collision is `u_2=0ms^-1`

The velocity of the first ball after the collision is `v_1=0ms^-1`

Therefore,

`8*3+15*0=8*0+15*v_2`

`15v_2=24`

`v_2=24/15=1.6ms^-1`

The velocity of the second ball after the collision is `v_2=1.6ms^-1`