Two identical cars are traveling at the same speed. One is heading due east and the other due north, as the drawing show. What is true regarding the kinetic energies and momenta of the cars?

The cars have the same kinetic energy, but different momentum.

if mass and velocity is the same, then KE is the same. Momentum is same magnitude, but in different directions.

Regarding the kinetic energies of the cars:

1. The kinetic energy of an object is given by the formula KE = (1/2)mv², where m is the mass of the object and v is its velocity.
2. Since both cars are traveling at the same speed, their velocities (v) are equal.
3. If the masses (m) of the cars are also equal, then their kinetic energies will be the same.

Regarding the momenta of the cars:

1. The momentum of an object is given by the formula p = mv, where m is the mass of the object and v is its velocity.
2. The momenta of the cars depend on the components of their velocities.
3. If the cars are traveling at the same speed (v), their momenta will depend on the angles at which they are traveling.
4. In the given scenario, one car is heading due east while the other is heading due north.
5. Since the cars are heading in perpendicular directions, their velocities are perpendicular vectors as well.
6. The vector sum of two perpendicular vectors is equal to the square root of the sum of their squares.
7. Therefore, the magnitude of the momentum vectors of the cars will be equal to the square root of the sum of the squares of their individual momenta.

To summarize:
- The kinetic energies of the cars will be the same if their masses are equal and they are traveling at the same speed.
- The momenta of the cars will have equal magnitudes, but their direction will depend on the angles at which they are traveling.

To determine what is true regarding the kinetic energies and momenta of the two cars, we need to consider their individual motions.

The kinetic energy of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. The momentum of an object is given by the formula p = m * v, where p is the momentum.

Since both cars are identical and traveling at the same speed, we can assume they have the same mass (m) and velocity (v).

Now, let's consider the kinetic energy of the cars. The car traveling due east will have a kinetic energy that is purely in the horizontal direction, since it is moving in that direction. On the other hand, the car traveling due north will have a kinetic energy that is purely in the vertical direction, since it is moving vertically. Since the cars have the same speed, their kinetic energies will be equal.

Next, let's consider the momenta of the cars. The car traveling due east will have a momentum in the positive horizontal direction, while the car traveling due north will have a momentum in the positive vertical direction. Again, since the cars have the same speed, their momenta will be equal.

In summary:
- The kinetic energies of the cars are equal.
- The momenta of the cars are equal.

This holds true because the cars have the same mass and velocity, even though they are traveling in different directions.