To find the mass of the second train, we can use the principle of conservation of momentum. The momentum before the collision must equal the momentum after the collision.
The formula for momentum (\(p\)) is:
\[ p = m \cdot v \]
where \(m\) is the mass and \(v\) is the velocity.
Let \(m_1\) be the mass of the first train, \(v_1\) be its velocity before the collision, \(m_2\) be the mass of the second train, and \(v_2\) be its velocity before the collision (which we will assume is 0 if it is at rest). After the collision, the two trains stick together and move with a common velocity (\(v_f\)).
Given:
- \(m_1 = 5000 , \text{kg}\)
- \(v_1 = 100 , \text{m/s}\)
- \(v_2 = 0 , \text{m/s}\) (assuming the second train is at rest)
- \(v_f = 50 , \text{m/s}\)
Using the conservation of momentum:
\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f \]
Substituting the values we know:
\[ 5000 , \text{kg} \cdot 100 , \text{m/s} + m_2 \cdot 0 = (5000 , \text{kg} + m_2) \cdot 50 , \text{m/s} \]
This simplifies to:
\[ 500000 , \text{kg} \cdot \text{m/s} = (5000 + m_2) \cdot 50 \]
Expanding the right side:
\[ 500000 = 250000 + 50m_2 \]
Now solve for \(m_2\):
\[ 500000 - 250000 = 50m_2 \] \[ 250000 = 50m_2 \] \[ m_2 = \frac{250000}{50} = 5000 , \text{kg} \]
Thus, the mass of the second train is:
D) 5,000 kg.
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