Question

Two approaching cars, coasting frictionlessly on a horizontal track, collide and couple. take the positive direction to the right. a) find the velocity of the coupled cars by taking the momenta relative to earth.

Answer 1

To find the velocity of the coupled cars by taking the momenta relative to earth, we need to use the principle of conservation of linear momentum.

Step-by-step explanation:

To find the velocity of the coupled cars by taking the momenta relative to earth, we need to use the principle of conservation of linear momentum. The principle states that the total momentum before the collision is equal to the total momentum after the collision.

Given the masses and velocities of the two cars, we can calculate their momenta. The momentum of an object is its mass multiplied by its velocity. Since the cars are approaching each other in a straight line, the momenta will have opposite signs.

We can add the momenta of the two cars together to find the total momentum before the collision. The total momentum after the collision will be equal to the total momentum before the collision, but with the masses now combined. We can solve for the final velocity of the coupled cars by dividing the total momentum after the collision by the mass of the combined cars.

In this case, let's assume the first car with a mass of 1200 kg is moving at 8.00 m/s due south, and the second car with a mass of 850 kg is moving at 17.0 m/s due west. Let's calculate the final velocity of the coupled cars.