contestada

A plane flies from base camp to lake a, 200 km away in the direction 20.0° north of east. after dropping off supplies it flies to lake b, which is 230 km at 30.0° west of north from lake
a. graphically determine the distance and direction from lake b to the base camp.

Respuesta :

Distance of lake a is 200 km at 20 degree north of east

distance between lake a and b is 230 km at 30 degree west of north

now the distance between base and lake b is given as

[tex]d = d_1 + d_2[/tex]

given that

[tex]d_1 = 200 cos20 i + 200 sin20 j[/tex]

[tex]d_1 = 187.94 i + 68.4 j[/tex]

[tex]d_2 = -230 sin30 i + 230 cos30 j[/tex]

[tex]d_2 = -115 i + 199.2 j[/tex]

now the total distance is

[tex]d = (187.94 - 115)i + (199.2 + 68.4)j [/tex]

[tex]d = 72.94 i + 267.6 j[/tex]

now the magnitude of the distance is given as

[tex]d = \sqrt{72.94^2 + 267.6^2}[/tex]

[tex]d = 277.4 [/tex]

also the direction is given as

[tex]\theta = tan^{-1}\frac{267.6}{72.94}[/tex]

[tex]\theta = 74.7 degree[/tex]

so it is 277.4 km at 74.7 degree North of East

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