Question

1. a train travels 36 miles east, then turns around and travels 60 miles west. find the: a. distance traveled by the train b. the displacement of the train 8. a bus travels 12 miles west, then 7 miles north. find the: a. distance traveled b. magnitude of the displacement

Explanation:

7a.

Step1: Define distance

Distance is total path length.
$36 + 60$

7b.

Step1: Define displacement

Displacement is net change in position. Let east be positive, west be negative.
$36-60$

8a.

Step1: Calculate distance

Distance is sum of path lengths.
$12 + 7$

8b.

Step1: Use Pythagorean theorem

Displacement forms right - triangle. Let west - east be x - axis and north - south be y - axis.
$\sqrt{12^{2}+7^{2}}$

Answer:

7a. 96 miles
7b. - 24 miles
8a. 19 miles
8b. $\sqrt{144 + 49}=\sqrt{193}\approx13.9$ miles