# Chapter 3 - Vectors and Coordinates Systems - Exercises and Problems - Page 78: 28

(a) At the end of the hike, the person is 100 meters lower compared to the starting point. (b) The magnitude of the net displacement is 5026 meters.

#### Work Step by Step

(a) The net vertical displacement is 200 m - 300 m which is -100 m. At the end of the hike, the person is 100 meters lower compared to the starting point. (b) We can add the two vectors to find the net displacement. $S_m+S_a = 500~m~east+5000~m~north-100~m~vertical$ We then find the magnitude $d$ of the net displacement; $d = \sqrt{(500~m)^2+(5000~m)^2+(-100~m)^2}$ $d = 5026~m$ The magnitude of the net displacement is 5026 meters.

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