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A moving freight car collides with an identical one that is at rest. If momentum is conserved, what happens to the second car after the collision? It attains the same speed as the first car. It moves at half the speed of the first car. It moves at twice the speed of the first car.

Answer :

For all elastic collisions we have

[tex]e = \frac{v_2 - v_1}{u_1 - u_2}[/tex]

[tex]e = 1 = \frac{v_2 - v_1}{u_1 - u_2}[/tex]

[tex]v_2 - v_1 = u - 0[/tex]

also by momentum conservation we will have

[tex]m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2[/tex]

since two cars are identical so we know that

[tex]m_1 = m_2 = m[/tex]

[tex]u + 0 = v_1 + v_2[/tex]

now by solving two equations we will have

[tex]v_2 = u[/tex]

[tex]v_1 = 0[/tex]

so the correct answer must be

It attains the same speed as the first car.

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