Serway & Jewett — Vectors: Problem 40

Ecotourists use their global positioning system indicator to determine their location inside a botanical garden as latitude \(0.002\,43^\circ\) south of the equator, longitude \(75.642\,38^\circ\) west. They wish to visit a tree at latitude \(0.001\,62^\circ\) north, longitude \(75.644\,26^\circ\) west. (a) Determine the straight-line distance and the direction in which they can walk to reach the tree as follows. First model the Earth as a sphere of radius \(6.37 \times 10^6 \text{ m}\) to determine the westward and northward displacement components required, in meters. Then model the Earth as a flat surface to complete the calculation. (b) Explain why it is possible to use these two geometrical models together to solve the problem.