15 points! A freight train is being assembled in a switching yard. Car 1 has a mass of 65,000 kg and moves with a velocity of +0.80m/s. Car 2 with a mass of 92,000 kg and has a velocity of +1.3m/s overtakes Car 1 and couples to it. Neglecting friction, calculate the final velocity of the two cars after they become coupled.

Solve using conservation of momentum.

We can solve this problem by applying the law of conservation of momentum, which states that for an isolated system, the total momentum must be conserved before and after the collision. Therefore, we can write:

So we can write:

[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]

where:

[tex]m_1 = 65,000 kg[/tex] is the mass of the first car

[tex]u_1 = +0.80 m/s[/tex] is the initial velocity of the first car

[tex]m_2 = 92,000 kg[/tex] is the mass of the second car

[tex]u_2 = +1.3 m/s[/tex] is the initial velocity of the second car

[tex]v[/tex] is the final combined velocity of the two cars after the collision

Re-arranging the equation and solving for v, we find the final velocity of the two cars:

[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(65,000)(0.80)+(92,000)(1.3)}{65,000+92,000}=+1.09 m/s[/tex]

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