An explorer in Antarctica leaves his shelter during a whiteout. He takes 39 step

Question

An explorer in Antarctica leaves his shelter during a whiteout. He takes 39 steps northeast, then 86 steps at an angle 60 degree north of west, then 47 steps due south. Assume his steps all have equal length. What is the magnitude of the displacement that will return the explorer to his shelter? Express your answer using two significant figures. R = steps What is the direction of the displacement that will return the explorer to his shelter? Express your answer using two significant figures. theta = degree east of south

Explanation / Answer

X = 39*cos45° - 86*sin30° = -15.43 steps
Y = 39*sin45° + 86*cos30° - 47 = 54.53 steps

a) M = [X² + Y²] = square root[-15.43^2+54.53^2]

=52.30 steps

b) = arctan[X/Y] =arctan[(-15.43/54.54)]

=17.38° E of S

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