Arvin the Ant travels 35 cm eastward,then 20 cm northward,and finally 10 cm westward.What is Arvin's direction of displacement with respect to his original position?

Question

Arvin the Ant travels 35 cm eastward,then 20 cm northward,and finally 10 cm westward.What is Arvin's direction of displacement with respect to his original position?
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Quizplus · Accepted Answer

Arvin's net displacement is the vector sum of his three displacements. The first displacement is 35 cm eastward, the second displacement is 20 cm northward, and the third displacement is 10 cm westward. The net displacement is therefore:```(35 cm, 0 cm) + (0 cm, 20 cm) + (-10 cm, 0 cm) = (25 cm, 20 cm)```The magnitude of the net displacement is:```sqrt(25^2 + 20^2) = 32.02 cm```The direction of the net displacement is:```arctan(20 cm / 25 cm) = 39.81°```Therefore, Arvin's direction of displacement with respect to his original position is 39.81° N of E, which is closest to choice A, 39° N of E.

Arvin the Ant Travels 35 Cm Eastward,then 20 Cm Northward,and