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 0.00293 degree south of the equator, longitude 75.64051 degrees west. They wish to visit a tree at latitude 0.00100 degree north, longitude 75.64502 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 times 10^6 m to determine the westward and northward displacement components required, in meters. displacement west m displacement north m Then model the Earth as a flat surface to complete the calculation. magnitude m direction degree north of west

Explanation / Answer

A) displacement west = 75.64502-75.64051

= 0.00451 degree west

= 0.00451*pi/180*6.37e6

= 501 m

Displacement north =0.00100+0.00293

= 0.00393 degree

= 0.00393*pi/180*6.37e6

=437 m

Net magnitude = sqrt(501^2+437^2)

= 665m

Direction = arctan(437/501)

41.1 degree north of west

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