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

Answer:

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

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 :

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$m_1u_1+m_2u_2-m_2v_2=m_1v_1$

$480\times 14.4+570\times 13.3-570\times 17.9=480v_1$

$v_1=8.93\ m/s$

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