QuestionJune 24, 2025

1. Jonah is walking along a trail. The trail heads east for 1350 meters, before turning north and continuing for 990 meters. At the end of the trail, what is Jonah's displacement vector? 2340 m, 31.0^circ east of north 1670 m. 36.3^circ north of east 1670 m, 36.3^circ east of north 2340 m. 31.0^circ north of east

1. Jonah is walking along a trail. The trail heads east for 1350 meters, before turning north and continuing for 990 meters. At the end of the trail, what is Jonah's displacement vector? 2340 m, 31.0^circ east of north 1670 m. 36.3^circ north of east 1670 m, 36.3^circ east of north 2340 m. 31.0^circ north of east
1. Jonah is walking along a trail. The trail heads east for 1350 meters, before turning north and continuing for 990 meters. At the end of the trail, what is Jonah's displacement vector? 2340 m, 31.0^circ east of north 1670 m. 36.3^circ north of east 1670 m, 36.3^circ east of north 2340 m. 31.0^circ north of east

Solution
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Answer

1670 m, 36.3^{\circ} north of east Explanation 1. Calculate the magnitude of displacement Use Pythagorean theorem: d = \sqrt{1350^2 + 990^2} d = \sqrt{1822500 + 980100} = \sqrt{2802600} = 1673.5 meters 2. Calculate the angle of displacement Use tangent function: \theta = \tan^{-1}\left(\frac{990}{1350}\right) \theta = \tan^{-1}(0.7333) = 36.3^{\circ} 3. Determine direction relative to east Since Jonah walks east first, then north, the angle is measured from east towards north.

Explanation

1. Calculate the magnitude of displacement<br /> Use Pythagorean theorem: $d = \sqrt{1350^2 + 990^2}$<br /> $d = \sqrt{1822500 + 980100} = \sqrt{2802600} = 1673.5$ meters<br /><br />2. Calculate the angle of displacement<br /> Use tangent function: $\theta = \tan^{-1}\left(\frac{990}{1350}\right)$<br /> $\theta = \tan^{-1}(0.7333) = 36.3^{\circ}$<br /><br />3. Determine direction relative to east<br /> Since Jonah walks east first, then north, the angle is measured from east towards north.
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