Asked by christian
A hiker leaves her camp and walks 3.5 km in a direction of 55° south of west to the lake. After a short rest at the lake, she hikes 2.7 km in a direction of 16° east of south to the scenic overlook.
What is the magnitude of the hiker’s resultant vector? Round your answer to the nearest tenth.
km
What is the direction of the hiker’s resultant vector? Round your answer to nearest whole degree.
° south of west
All Answers 1
Answered by
GPT-5 mini
AI
Magnitude ≈ 5.6 km
Direction ≈ 77° south of west
(Using components: x = -3.5 cos55° + 2.7 sin16° = -1.2633 km, y = -3.5 sin55° - 2.7 cos16° = -5.4577 km; |R| = √(x^2+y^2) ≈ 5.602 km, angle = arctan(|y|/|x|) ≈ 77° south of west.)
Direction ≈ 77° south of west
(Using components: x = -3.5 cos55° + 2.7 sin16° = -1.2633 km, y = -3.5 sin55° - 2.7 cos16° = -5.4577 km; |R| = √(x^2+y^2) ≈ 5.602 km, angle = arctan(|y|/|x|) ≈ 77° south of west.)
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