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)

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)
Responses

16 kg-m/s northeast

8 kg-m/s southwest

16 kg-m/s southwest

8 kg-m/s northeast

abc or d

GPT 3.5 · Answer

The momentum of the first object is 12 kg-m/s northeast and the momentum of the second object is 4 kg-m/s southwest. When they collide and stick together, their momenta combine.

To combine the momenta, we can simply add the magnitudes of the momenta together, while considering the direction.

The momentum of the first object (12 kg-m/s northeast) can be represented as 12 kg-m/s at an angle of 45 degrees (northeast is 45 degrees between north and east).

The momentum of the second object (4 kg-m/s southwest) can be represented as 4 kg-m/s at an angle of 225 degrees (southwest is 135 degrees between south and west, but since it needs to be measured from the positive x-axis, we subtract 90 degrees to get 225 degrees).

To add the momenta, we can convert them into their x- and y-components, and then add those components together.

The x-component of the momentum of the first object is given by:

12 kg-m/s * cos(45 degrees) = 12 kg-m/s * 0.707 ≈ 8.48 kg-m/s

The y-component of the momentum of the first object is given by:

12 kg-m/s * sin(45 degrees) = 12 kg-m/s * 0.707 ≈ 8.48 kg-m/s

The x-component of the momentum of the second object is given by:

4 kg-m/s * cos(225 degrees) = 4 kg-m/s * -0.707 ≈ -2.83 kg-m/s

The y-component of the momentum of the second object is given by:

4 kg-m/s * sin(225 degrees) = 4 kg-m/s * -0.707 ≈ -2.83 kg-m/s

Now we can add the x-components and y-components separately:

8.48 kg-m/s + (-2.83 kg-m/s) = 5.65 kg-m/s (x-component)

8.48 kg-m/s + (-2.83 kg-m/s) = 5.65 kg-m/s (y-component)

To get the magnitude of the momentum after the collision, we can use Pythagorean theorem:

√(5.65 kg-m/s)^2 + (5.65 kg-m/s)^2 = √(31.96 + 31.96) ≈ √63.92 ≈ 7.99 kg-m/s

The direction of the momentum after the collision can be determined by finding the angle it makes with the positive x-axis. We can use inverse tangent to find this angle:

tan^(-1)(5.65 kg-m/s / 5.65 kg-m/s) ≈ 45 degrees

Therefore, the momentum after the collision is 7.99 kg-m/s northeast.

So, the correct response is: 8 kg-m/s northeast