One object is traveling northeast with a momentum of 12 kg-m/s, while a second object is traveling southwest on the same path as the first object with a momentum of 4 kg-m/s. When the two objects collide, they stick together.

Question

What is the momentum after their collision? (1 point)
O 16 kg-m/s northeast
• 8 kg-m/s southwest
• 16 kg-m/s southwest
• 8 kg-m/s northeast

Answer 1

To determine the momentum after the collision, we first need to analyze the momentum of both objects before the collision.

1. Object 1:

   • Momentum = 12 kg·m/s (northeast)

2. Object 2:

   • Momentum = 4 kg·m/s (southwest)
   • Since southwest is in the opposite direction of northeast, we can treat this momentum as a negative value for our calculations.

Now, let's represent northeast as the positive direction. Therefore, we can represent the momenta of both objects in terms of vector quantities:

• Momentum of Object 1 (northeast) = +12 kg·m/s
• Momentum of Object 2 (southwest) = -4 kg·m/s

Now, we can find the total momentum before the collision:

\[ \text{Total Momentum} = \text{Momentum of Object 1} + \text{Momentum of Object 2} \] \[ = 12 , \text{kg·m/s} + (-4 , \text{kg·m/s}) = 12 , \text{kg·m/s} - 4 , \text{kg·m/s} = 8 , \text{kg·m/s} \]

The total momentum before the collision is 8 kg·m/s in the northeast direction.

Since the two objects stick together after the collision, the momentum after the collision remains the same as the total momentum before the collision. Thus, we can conclude that the momentum after their collision is:

8 kg-m/s northeast

This means the correct answer to the question is:

• 8 kg-m/s northeast