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?

To determine what is true regarding the kinetic energies and momenta of the cars, we need to consider the concept of vectors and their components.

Kinetic Energy:
The kinetic energy of an object is defined as ½ mv², where m is the mass of the object and v is its velocity. Since both cars are traveling at the same speed, their kinetic energies will be the same.

Momentum:
The momentum of an object is defined as the product of its mass and velocity (p = m * v). In vector terms, momentum has both magnitude and direction. To find the total momentum of the two cars, we need to find the vector sum of their momenta.

In the given scenario, one car is heading due east, and the other is heading due north. We can represent their velocities as vectors by breaking them into their x and y components.

Let's assume the speed of each car is represented by "v."

Car heading due east:
Velocity: v = (v_x, 0) (Only the x-component)
Momentum: p_east = m * (v_x, 0)

Car heading due north:
Velocity: v = (0, v_y) (Only the y-component)
Momentum: p_north = m * (0, v_y)

Since the cars are traveling at the same speed, their masses will cancel out when comparing their momenta. Therefore, the magnitude of their momenta will be the same.

Now, regarding the direction of the momenta, the car heading due east will have its momentum entirely in the positive x-direction (east). The car heading due north will have its momentum entirely in the positive y-direction (north). Thus, the momenta of the cars will be perpendicular to each other.

To summarize:
- The kinetic energies of the cars will be the same since they are traveling at the same speed.
- The momenta of the cars will have the same magnitude but will be perpendicular to each other.