Question

Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 1.62 ✕ 105 kg and a velocity of (0.30 m/s)î, and the second having a mass of 1.11 ✕ 105 kg and a velocity of −(0.12 m/s)î. What is their final velocity (in m/s)? (Express your answer in vector form.)

Answer 1

`V = (0.129\ m/s)\ i`

Step-by-step explanation:

It is given that,

Mass of the car 1,
`m_1=1.62* 10^5\ kg`

Initial speed of the car 1,
`u_1=0.3\ m/s i`

Mass of the car 2,
`m_2=1.11* 10^5\ kg`

Initial speed of the car 2,
`u_2=-0.12\ m/s i`

It is mentioned that train cars are coupled together by being bumped into one another. Let V is the final velocity of the train cars after the collision. It can be calculated using the conservation of linear momentum as :

`m_1u_1+m_2u_2=(m_1+m_2)V`

`V=(m_1u_1+m_2u_2)/(m_1+m_2)`

`V=(1.62* 10^5* 0.3+1.11* 10^5* (-0.12))/(1.62* 10^5+1.11* 10^5)`

`V = (0.129\ m/s)\ i`

So, the final speed of the coupled train cars is 0.129 m/s towards x axis. Hence, this is the required solution.