Question

1. a police officer is driving southbound on the highway at a speed of 24 meters per second. he sees a yellow car driving northbound. from inside the moving police car, the officer measures the yellow cars speed as 59 meters per second. to an observer on the side of the road, what is the yellow cars velocity?

24 m/s
83 m/s
59 m/s
35 m/s

Explanation:

Step1: Define the velocities

Let the velocity of the police car \(v_p=- 24\ m/s\) (south - bound, so negative direction) and the relative velocity of the yellow car with respect to the police car \(v_{y/p}=59\ m/s\) (north - bound, positive direction). The formula for relative velocity is \(v_{y/p}=v_y - v_p\), where \(v_y\) is the velocity of the yellow car with respect to the observer on the side of the road.

Step2: Solve for \(v_y\)

Rearrange the formula \(v_y=v_{y/p}+v_p\). Substitute the values: \(v_y = 59+( - 24)\)

$$v_y=59 - 24$$

$$v_y = 35\ m/s$$

Answer:

35 m/s