Question

A 480 kg car moving at 14.4 m/s hits from behind another car moving at 13.3 m/s in the same direction. If the second car has a mass of 570 kg and a new speed of 17.9 m/s, what is the velocity of the first car after the collision?

Answer 1

Velocity of the first car after the collision,
`v_1=8.93\ m/s`

Step-by-step explanation:

It is given that,

Mass of the car,
`m_1 = 480\ kg`

Initial speed of the car,
`u_1 = 14.4\ m/s`

Mass of another car,
`m_2 = 570\ kg`

Initial speed of the second car,
`u_2 = 13.3\ m/s`

New speed of the second car,
`v_2 = 17.9\ m/s`

Let
`v_1` is the final speed of the first car after the collision. The total momentum of the system remains conserved, Using the conservation of momentum to find it as :

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

`m_1u_1+m_2u_2-m_2v_2=m_1v_1`

`480* 14.4+570* 13.3-570* 17.9=480v_1`

`v_1=8.93\ m/s`

So, the velocity of the first car after the collision is 8.93 m/s. Hence, this is the required solution.