Question

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. what is the momentum after their collision? (1 point)

16 kg - m/s northeast

16 kg - m/s southwest

8 kg - m/s southwest

8 kg - m/s northeast

Explanation:

Step1: Define directions

Let northeast be the positive - direction and southwest be the negative - direction.

Step2: Calculate the total initial momentum

The first object has a momentum $p_1 = 12\ kg\cdot m/s$ (positive as it is moving northeast) and the second object has a momentum $p_2=- 4\ kg\cdot m/s$ (negative as it is moving southwest). The total initial momentum $p_{total}=p_1 + p_2$.
$p_{total}=12+( - 4)=8\ kg\cdot m/s$

Step3: Apply the law of conservation of momentum

In a closed - system (the two - object system here), the total momentum before the collision is equal to the total momentum after the collision. Since the total initial momentum is $8\ kg\cdot m/s$ in the positive (northeast) direction, the total momentum after the collision is also $8\ kg\cdot m/s$ in the northeast direction.

Answer:

8 kg - m/s northeast