Question

Cameron drives his car from his house 22 miles north, then turns

and drives 15 miles west to a friend's house. He stays there for an hour and
then drives 48 miles south to the soccer field. He plays a game and then
drives 5 miles east to have dinner with his teammates. What is Cameron's
distance and displacement? Show all work on the back of this page or on a
separate sheet of paper. (Hint: Draw a picture!!)

Answer 1

Cameron's distance is 90 miles and his displacement is approximately 27.9 miles to the southwest.

Step-by-step explanation:

To find Cameron's distance and displacement, let's consider the directions he travels in. Cameron drives 22 miles north, then 15 miles west, then 48 miles south, and finally 5 miles east. To calculate the distance, we add up the distances traveled in each direction. Distance = 22 + 15 + 48 + 5 = 90 miles.

To calculate the displacement, we need to consider the net direction and magnitude. We can find the net east-west and north-south distances. Displacement = (15 - 5) miles west + (48 - 22) miles south = 10 miles west + 26 miles south. Using Pythagoras' theorem, we can find the magnitude of the displacement: sqrt[(10)^2 + (26)^2] = sqrt[100 + 676] = sqrt[776] ≈ 27.9 miles. Therefore, Cameron's displacement is approximately 27.9 miles to the southwest.