question 10 (5 points)\nlisten\na jaguar is initially 20 km n of la pedo. first is walks 30 km e and then…

Explanation:

Step1: Analyze vertical displacement

The initial north - ward displacement is $y_1 = 20$ km and the south - ward displacement is $y_2=40$ km. The net vertical displacement $y=y_1 - y_2=20 - 40=- 20$ km (negative means south - ward). The horizontal displacement $x = 30$ km (east - ward).

Step2: Calculate magnitude of displacement

Use the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 30$ km and $y=-20$ km. $d=\sqrt{30^{2}+(-20)^{2}}=\sqrt{900 + 400}=\sqrt{1300}\approx36.1$ km.

Step3: Calculate direction of displacement

Use the tangent function $\theta=\tan^{-1}\left(\frac{\vert y\vert}{x}\right)$. Substitute $x = 30$ km and $\vert y\vert = 20$ km. $\theta=\tan^{-1}\left(\frac{20}{30}\right)\approx36.9^{\circ}$. The direction is [E $36.9^{\circ}$ S].

Answer:

$36.1$ km [E $36.9^{\circ}$ S]