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Answer:
To find the total momentum of the system before the collision, we need to calculate the momentum of each cart and then sum them, taking into account their directions.
Given:
- Mass of the first cart (\(m_1\)) = 10 kg
- Velocity of the first cart (\(v_1\)) = 5 m/s
- Mass of the second cart (\(m_2\)) = 15 kg
- Velocity of the second cart (\(v_2\)) = -2 m/s (negative because it is moving in the opposite direction)
The momentum of the first cart (\(p_1\)) is:
\[ p_1 = m_1 \times v_1 = 10 \, \text{kg} \times 5 \, \text{m/s} = 50 \, \text{kg·m/s} \]
The momentum of the second cart (\(p_2\)) is:
\[ p_2 = m_2 \times v_2 = 15 \, \text{kg} \times (-2) \, \text{m/s} = -30 \, \text{kg·m/s} \]
The total momentum of the system before the collision (\(p_{\text{total}}\)) is:
\[ p_{\text{total}} = p_1 + p_2 = 50 \, \text{kg·m/s} + (-30) \, \text{kg·m/s} = 20 \, \text{kg·m/s} \]
Therefore, the total momentum of the system before the collision is 20 kg·m/s.