Question

A police car in a high-speed chase is traveling north on a two-lane highway at 35.0 m/s. In the southbound lane of the same highway, an SUV is moving at 18.0 m/s. Take the positive x-direction to be toward the north.

a)Find the x-velocity of the police car relative to the SUV.
b) Find the x-velocity of the SUV relative to the police car.

Answer 1

The x-velocity of the police car relative to the SUV is 53.0 m/s, and the x-velocity of the SUV relative to the police car is -53.0 m/s.

Step-by-step explanation:

a) To find the x-velocity of the police car relative to the SUV, we need to determine the difference in their velocities in the x-direction. Since both vehicles are moving in opposite directions along the same highway, their velocities will be subtracted. The x-velocity of the police car relative to the SUV is therefore 35.0 m/s - (-18.0 m/s) = 53.0 m/s.

b) Similarly, to find the x-velocity of the SUV relative to the police car, we need to determine the difference in their velocities in the x-direction. Since both vehicles are moving in opposite directions along the same highway, their velocities will be subtracted.

The x-velocity of the SUV relative to the police car is therefore (-18.0 m/s) - 35.0 m/s = -53.0 m/s, indicating that the SUV is moving in the opposite direction with respect to the police car.