Question

current attempt in progress
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?

they have the same kinetic energies, but different momenta.
they have different kinetic energies and different momenta.
they have different kinetic energies, but the same momenta.
they have the same kinetic energies and the same momenta.

Explanation:

Step1: Analyze kinetic energy formula

The formula for kinetic energy is \(K = \frac{1}{2}mv^{2}\). Since the cars are identical (\(m\) is the same) and have the same speed (\(v\) is the same), substituting into the formula gives \(K_1=\frac{1}{2}mv^{2}\) and \(K_2=\frac{1}{2}mv^{2}\), so \(K_1 = K_2\).

Step2: Analyze momentum formula

The formula for momentum is \(\vec{p}=m\vec{v}\). Momentum is a vector quantity. One car has velocity \(\vec{v}\) in the east - direction (\(\vec{p}_1 = m\vec{v}\text{(east)}\)) and the other has velocity \(\vec{v}\) in the north - direction (\(\vec{p}_2=m\vec{v}\text{(north)}\)). Since their directions are different, \(\vec{p}_1
eq\vec{p}_2\).

Answer:

They have the same kinetic energies, but different momenta.