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

Answer:

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

Explanation:

It is given that,

Mass of the car 1, $m_1=1.62\times 10^5\ kg$

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

Mass of the car 2, $m_2=1.11\times 10^5\ kg$

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 :

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

$V=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}$

$V=\dfrac{1.62\times 10^5\times 0.3+1.11\times 10^5\times (-0.12)}{1.62\times 10^5+1.11\times 10^5}$

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

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