Question

A ball with a mass of `2 kg` is rolling at `3 m/s` and elastically collides with a resting ball with a mass of `4 kg`. What are the post-collision velocities of the balls?

Answer 1

Speed of moving ball after collision `"= 1 m/s"` (in the direction opposite to it’s initial direction of motion)
Speed of resting ball after collision `"= 2 m/s"`

Explanation:

Apply conservation of linear momentum

`"Initial total momentum = Final total momentum"`

`m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2`

`(2 × 3) + (4 × 0) = 2v_1 + 4v_2`

`6 = 2v_1 + 4v_2`

Didvide both sides by `2`

`3 = v_1 + 2v_2 color(white)(xxxxxxxxxxxxxxxx)(1)`

Now, use formula of coefficient of restitution (`e`)

`e = (v_2 - v_1)/(u_1 - u_2)`

For an elastic collision `e = 1`

`1 = (v_2 - v_1) / (3 - 0)`

`v_2 - v_1 = 3 color(white)(xxxxxxxxxxxxxxxxx)(2)`

Add equations `"(1) & (2)"`

`3 + 3 = v_1 + 2v_2 + v_2 - v_1`

`6 = 3v_2`

`color(blue)(v_2 = "2 m/s")`

Substitute `v_2 = "2 m/s"` in equation `(1)`

`3 = v_1 + (2 × "2 m/s")`

`color(blue)(v_1 = -"1 m/s")`