Question

5 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 jonahs displacement vector? 2340 m, 31.0° north of east 2340 m, 31.0° east of north 1670 m, 36.3° east of north 1670 m, 36.3° north of east

Explanation:

Step1: Calculate the magnitude of the displacement vector

The two - part motion forms a right - triangle. Let \(x = 1350m\) (east - west component) and \(y=990m\) (north - south component).
By the Pythagorean theorem \(d=\sqrt{x^{2}+y^{2}}\).
Substitute \(x = 1350\) and \(y = 990\):
\(d=\sqrt{1350^{2}+990^{2}}=\sqrt{1822500 + 980100}=\sqrt{2802600}\approx1670m\)

Step2: Calculate the direction of the displacement vector

The direction \(\theta\) (measured from the north) is given by \(\tan\theta=\frac{x}{y}\) (since \(x\) is the adjacent side to the angle measured from the north and \(y\) is the opposite side).
\(\tan\theta=\frac{1350}{990}=\frac{15}{11}\approx1.364\)
\(\theta=\arctan(1.364)\approx36.3^{\circ}\) east of north

Answer:

1670 m, \(36.3^{\circ}\) east of north (the third option)