Question

A car moving with an initial speed v collides with a second stationary car that is one-half as massive. After the collision the first car moves in the same direction as before with a speed v/3. Find the final speed of the second car.

Answer 1

4v/3

Step-by-step explanation:

Assume elastic collision by the law of momentum conservation:

`m_1v = m_1v_1 + m_2v_2`

where v is the original speed of car 1, v1 is the final speed of car 1 and v2 is final speed of car 2. m1 and m2 are masses of car 1 and car 2, respectively

Substitute
`m_2 = m_1/2 \& v_1 = v/3`

`m_1v = (m_1v)/(3) + (m_1v_2)/(2)`

Divide both side by
`m_1`, then multiply by 6 we have

`6v = 2v + 3v_2`

`3v_2 = 4v`

`v_2 = (4v)/(3)`

So the final speed of the second car is 4/3 of the first car original speed