Two cars started at the same position and were driven through a city using different streets. the red car traveled north 2 miles, then east 4 miles, and then south 6 miles. the green car traveled south 4 miles and then east 4 miles. both cars ended at the same location.

which best compares the motion of the cars?

a. the red car traveled a shorter distance, but the displacement of the cars was equal.
b. the green car traveled a shorter distance, but the displacement of the cars was equal.
c. the green car had a shorter displacement, but the distance traveled by the cars was equal.
d. the red car had a shorter displacement, but the distance traveled by the cars was equal.

b. The green car traveled a shorter distance, but the displacement of the cars was equal.

Explanation:

Let's keep in mind the difference between distance and displacement:

- distance: it is just the total distance covered, it does not depend on the direction

- displacement: it is the difference between the final position and the initial position

The distance traveled by the red car is: 2 miles + 4 miles + 6 miles =12 miles

The distance traveled by the green car is: 4 miles + 4 miles = 8 miles

Therefore, the green car traveled a shorter distance. However, the displacement of the two cars is the same, because they both start at the same position and they both end at the same location, so option b) is the correct one.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west