Ecotourists use their global positioning system indicator to determine their loc

Question

Ecotourists use their global positioning system indicator to determine their location inside a botanical garden as latitude 0.004 40 degree south of the equator, longitude 75.640 95 degrees west. They wish to visit a tree at latitude 0.001 04 degree north, longitude 75.644 35 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.

displacement west


displacement north

Now model the Earth as a flat surface to complete the calculation.
magnitude m
direction

Explanation / Answer

difference in latitude=0.00104-0.00400=-0.00296 difference in longitude= 75.64435-75.64095=.00340 radius =6.37*10^6 m which is equal to 360 latitude and longitude so displacement west=-104.75 m so displacement north =120.32 m if we consider the earth flat surface surface area is same so earth will be square having side =(4*3.14*6.37*10^6)^1/2 =22.58*10^6 m so side 22.58*10^6 m has 360 degree latitude and longitude displacement west=-185.65 m so displacement north =213.25 m

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