Question

Two identical cars are traveling at the same speed. One is heading due east and the other due north, as the drawing shows. Which statement is true regarding the kinetic energies and momenta of the cars?A) They have the same kinetic energies, but different momenta.B) They have different kinetic energies, but the same momenta.C) They have the same kinetic energies and the same momenta.D) They have different kinetic energies and different momenta.

Answer 1

Answer:

A) They have the same kinetic energies, but different momenta.

Explanation:

Before answering, let's remind that:

- Kinetic energy is a scalar quantity, which is given by:

$K=\frac{1}{2}mv^2$

where m is the mass of the object and v is the speed.

- Momentum is a vector quantity, whose magnitude is given by:

$p=mv$

where m is the mass of the object and v is the velocity, and whose direction is the same as the velocity.

By looking at the two definitions, we can say that:

- the two cars have same kinetic energy, because they have same mass and same speed

- The two cars have different momenta, because they do not have same velocity (in fact, their directions are different, since one is heading east and the other one is heading north)