Question

you walk west 30 km and then south 40 km. determine the total distance and the displacement at the end of your walk. (1 point)
the distance is 70 km and the displacement is 50 km northeast, using the pythagorean theorem.
the distance is 50 km and the displacement is 70 km southwest, using the pythagorean theorem.
the distance is 70 km southwest and the displacement is 50 km, using the pythagorean theorem.
the distance is 70 km and the displacement is 50 km southwest, using the pythagorean theorem.

Explanation:

Step1: Calculate the total distance

The total distance is the sum of the two paths walked.
\(d = 30+40=70\) km

Step2: Calculate the displacement

The two paths (west - 30 km and south - 40 km) are perpendicular. Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 30\) km and \(b=40\) km.
\(c=\sqrt{30^{2}+40^{2}}=\sqrt{900 + 1600}=\sqrt{2500}=50\) km.
The direction is southwest (since one moves west and then south).

Answer:

The distance is \(70\) km and the displacement is \(50\) km southwest, using the Pythagorean theorem. So the correct option is: The distance is \(70\) km and the displacement is \(50\) km southwest, using the Pythagorean theorem.