Question

A ball with a mass of `2kg` moving at `1 m/s` hits a still ball with a mass of `6 kg`. If the first ball stops moving, how fast is the second ball moving?

Answer 1

`~~0.33 \ "m/s"`

Explanation:

We use the conservation of momentum equation, which states that,

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

• `m_1,m_2` are the masses of the two objects

• `u_1,u_2` are the initial velocities of the two objects

• `v_1,v_2` are the final velocities of the two objects

Since we want to know how fast is the second ball moving after the collision, we need to solve for `v_2`, and we rearrange the equation into:

`v_2=(m_1u_1+m_2u_2-m_1v_1)/m_2`

Now, we can plug in values into the equation and we get,

`v_2=(2 \ "kg"*1 \ "m/s"+6 \ "kg"*0 \ "m/s"-2 \ "kg"*0 \ "m/s")/(6 \ "kg")`

`=(2 \ "kg m/s"+0 \ "kg m/s"-0 \ "kg m/s")/(6 \ "kg")`

`=(2color(red)cancelcolor(black)"kg""m/s")/(6color(red)cancelcolor(black)"kg")`

`=1/3 \ "m/s"`

`~~0.33 \ "m/s"`