Question

6000 kg train moving 5 m/sec to east collides with 5000 kg train moving 3 m/sec to west. What is their velocity

Answer 1

The final velocity is 1.37 m/s east

Explanation:

We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two trains must be conserved before and after the collision.

So we can write:

$p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v$

where:

$m_1 = 6000 kg$ is the mass of the first train

$u_1 = 5 m/s$ is the initial velocity of the first train (we take east as positive direction)

$m_2 = 5000 kg$ is the mass of the second train

$u_2 = -3 m/s$ is the initial velocity of the second train

$v$ is the final combined velocity of the two trains

Re-arranging the equation and substituting the values, we find:

$v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(6000)(5)+(5000)(-3)}{6000+5000}=1.37 m/s$

And the positive sign indicates their final direction is east.

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