To solve this problem, we need to calculate the total momentum of the bus and the car after the collision. Here are the steps to find the solution:
1. Understand momentum: Momentum (p) is the product of mass (m) and velocity (v), given by the formula [tex]\( p = m \cdot v \)[/tex].
2. Calculate the momentum of the bus:
- Mass of the bus ([tex]\(m_{\text{bus}}\)[/tex]): [tex]\( 1.5 \times 10^3 \)[/tex] kg
- Velocity of the bus ([tex]\(v_{\text{bus}}\)[/tex]): [tex]\( +20 \)[/tex] m/s
- Momentum of the bus ([tex]\(p_{\text{bus}}\)[/tex]): [tex]\( p_{\text{bus}} = m_{\text{bus}} \cdot v_{\text{bus}} = 1.5 \times 10^3 \, \text{kg} \times 20 \, \text{m/s} = 30,000 \, \text{kg} \cdot \text{m/s} \)[/tex]
3. Calculate the momentum of the car:
- Mass of the car ([tex]\(m_{\text{car}}\)[/tex]): [tex]\( 9.5 \times 10^2 \)[/tex] kg
- Velocity of the car ([tex]\(v_{\text{car}}\)[/tex]): [tex]\( -26 \)[/tex] m/s
- Momentum of the car ([tex]\(p_{\text{car}}\)[/tex]): [tex]\( p_{\text{car}} = m_{\text{car}} \cdot v_{\text{car}} = 9.5 \times 10^2 \, \text{kg} \times (-26) \, \text{m/s} = -24,700 \, \text{kg} \cdot \text{m/s} \)[/tex]
4. Calculate the total momentum after the collision:
- Total momentum after the collision ([tex]\(p_{\text{total}}\)[/tex]): [tex]\( p_{\text{total}} = p_{\text{bus}} + p_{\text{car}} = 30,000 \, \text{kg} \cdot \text{m/s} + (-24,700 \, \text{kg} \cdot \text{m/s}) = 5,300 \, \text{kg} \cdot \text{m/s} \)[/tex]
The total momentum after the collision is [tex]\( 5,300 \, \text{kg} \cdot \text{m/s} \)[/tex], which corresponds to option C.
So, the correct answer is:
C. [tex]\( 5.3 \times 10^3 \)[/tex] kilogram meters/second
