Question

a family on a road trip has to take a detour off the main highway. in doing so, they travel 27 km n and then turn to travel 11 km e. what is their displacement while on the detour? (2.2) (a) 32 km n 70° w (b) 38 km n 68° e (c) 29 km n 22° e (d) 35 km n 68° w

Explanation:

Step1: Resolve displacements into components

Let the north - south component be $y$ and east - west component be $x$. The north - ward displacement $d_N=27$ km and east - ward displacement $d_E = 11$ km.

Step2: Use the Pythagorean theorem for magnitude

The magnitude of the displacement $d=\sqrt{d_N^{2}+d_E^{2}}=\sqrt{27^{2}+11^{2}}=\sqrt{729 + 121}=\sqrt{850}\approx29$ km.

Step3: Find the direction

The angle $\theta$ measured north of east is given by $\tan\theta=\frac{d_N}{d_E}=\frac{27}{11}\approx2.4545$. So, $\theta=\arctan(2.4545)\approx68^{\circ}$ N of E.

Answer:

(c) 29 km [N 68° E]