Hello Jordan,
In the first 30 minutes (or 30min*60s/min = 1800 seconds) the hiker walks:
2 m/s * 1800 s = 3600 meters north (or upward on a piece of paper) ---- I modified the units of time in order to match the units of speed.
In the following hour (60min*60s/min = 3600 second) the hiker walks:
1 m/s * 3600 s = 3600 meters west (or left on our piece of paper)
a) in total the hiker walks 3600m + 3600m = 7200m
b) Now, we make a triangle with the two legs that the hiker walked, and drawing a line between the start and the finish. That line is the displacement from the campsite (distance from the starting point). As this can be treated as the hypotenuse of the triangle, we calculate it's length using the Pythagorean theorem or the distance formula (same thing).
a^2 + b^2 = c^2 ---- where a is the distance walked north, b is the distance walked west, and c is the displacement from the campsite.
3600^2 + 3600^2 = c^2
squareroot(1.296*10^7 + 1.296*10^7) = c = 5091.2 meters of displacement (ignoring significant figures)
c) distance is the literal amount of walking that the person did. displacement is the straight-line distance between the start point and the end point.
In this case, the displacement is calculated using the Pythagorean theorem, because the geometry of the situation lent itself to that as we needed to make a triangle. This will not always be the case, so it is helpful to draw out the path as you move through each leg of travel. Then, draw your displacement vector and figure out how you can solve for it's length based on what you have.
Hopefully this helps. Cheers!
Justin
