To determine the momentum of the two-object system after the collision, we need to apply the law of conservation of momentum. Here’s a detailed, step-by-step solution to solve this problem:
1. Understand the Law of Conservation of Momentum: This law states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision, provided no external forces act on it.
2. Calculate the Initial Momentum:
- Momentum is defined as the product of mass and velocity ([tex]\( p = mv \)[/tex]).
Before the collision, we should calculate the momentum for each object:
- For object A:
- Mass ([tex]\( m_A \)[/tex]) = 200 kg
- Velocity ([tex]\( v_A \)[/tex]) = 15 m/s
- Momentum of A ([tex]\( p_A \)[/tex]) = mass [tex]\(\times\)[/tex] velocity = [tex]\( 200 \times 15 = 3000 \)[/tex] kg·m/s
- For object B:
- Mass ([tex]\( m_B \)[/tex]) = 150 kg
- Velocity ([tex]\( v_B \)[/tex]) = -10 m/s (negative sign indicates direction opposite to that of object A)
- Momentum of B ([tex]\( p_B \)[/tex]) = mass [tex]\(\times\)[/tex] velocity = [tex]\( 150 \times (-10) = -1500 \)[/tex] kg·m/s
3. Calculate the Total Initial Momentum:
- Total initial momentum ([tex]\( p_{\text{total}} \)[/tex]) = momentum of A + momentum of B
- Therefore, [tex]\( p_{\text{total}} = p_A + p_B = 3000 + (-1500) = 1500 \)[/tex] kg·m/s
4. Final Momentum Calculation:
- In a collision where the objects stick together, the total momentum of the system after the collision will be the same as the total momentum before the collision (by the conservation of momentum).
- Therefore, the momentum of the combined mass after the collision is 1500 kg·m/s.
So, the momentum of the object after the collision is [tex]\( 1500 \)[/tex] kg·m/s.
Therefore, the correct answer is:
[tex]\[ \boxed{1,500 \; \text{kg·m/s}} \][/tex]
