60. Ecotourists use their global positioning system indicator to determine their

Question

60. Ecotourists use their global positioning system indicator to determine their location inside a botanical garden as latitude 0.002 43 degree south of the equator, longitude 75.642 38 degrees west. They wish to visit a tree at latitude 0.001 62 degree north, longitude 75.644 26 degrees 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 Mm 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.

With explanation please..Thanks!

Explanation / Answer

60.

given

lat = 0.00243 deg S

lon = 75.64238 deg W

taRGET tree

lat1 = 0.00162 N

lon1 = 75.64426 W

a. R = 6.37*10^6 m

westward distance = (75.64426 - 75.64238)*pi*6.37*10^6*cos(0.00243)/180 = 209.0136497 m

northward distance = (0.00162 + 0.00243)*pi*6.37*10^6/180 = 450.268767 m

then using earth as flat, total distance = sqrt(x^2 + y^2) = 496.415822

direction = arctan(y/x) = 65.099 deg north of west

b. we can use flat earth theory because once we have found distances aliong the curvature of earth, then for small distances this can be though of as a component on a flat plane

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