An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60 degrees north of west, then 50 steps due south.Assume his steps all have equal length. Save him from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut. ...?

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22-11-2016
Mathematics

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An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60 degrees north of west, then 50 steps due south.Assume his steps all have equal length. Save him from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut. ...?

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Аноним Аноним · Answer 1 · 2016-11-25T04:39:25+01:00

Setting the coordinate system: positive x points to the east and positive y points to the north. This can be solved by vector addition.

A = <40cos(45), 40sin(45)>
B = <-60cos(60), 60sin(60)>
C = <0, -50>

R = A + B + C = <-1.72, 80.25>

The displacement that needs to return him is by the vector -R.

Therefore, <1.72, -80.25>

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