Question

9 a team of biologists are tracking the motion of a mountain lion. the lion walks north for 880 meters, then turns and walks west for 1760 m. what is the displacement vector for the lions motion? 1970 m, 63.4° north of west 2640 m, 72.2° north of west 1970 m, 63.4° west of north 2640 m, 72.2° west of north

Explanation:

Step1: Calculate the magnitude of displacement

The two - motion vectors (north and west) are perpendicular. Use the Pythagorean theorem \(d=\sqrt{d_{1}^{2}+d_{2}^{2}}\), where \(d_{1} = 880m\) (north) and \(d_{2}=1760m\) (west).
\(d=\sqrt{880^{2}+1760^{2}}=\sqrt{774400 + 3097600}=\sqrt{3872000}\approx1970m\)

Step2: Calculate the direction of displacement

Use the tangent function \(\tan\theta=\frac{d_{2}}{d_{1}}\) (opposite side \(d_{2}\) (west) over adjacent side \(d_{1}\) (north)). \(\tan\theta=\frac{1760}{880} = 2\), so \(\theta=\arctan(2)\approx63.4^{\circ}\). The direction is west of north.

Answer:

1970 m, \(63.4^{\circ}\) west of north (the third option)