Question

a mountain - climbing expedition establishes two intermediate camps, labeled a and b in the drawing, above the base camp. what is the magnitude $delta r$ of the displacement between camp a and camp b?

Explanation:

Step1: Find horizontal displacement

The horizontal displacement $\Delta x=19600 - 11200=8400$ m.

Step2: Find vertical displacement

The vertical displacement $\Delta y = 4900 - 3200 = 1700$ m.

Step3: Use Pythagorean theorem

The magnitude of the displacement $\Delta r=\sqrt{\Delta x^{2}+\Delta y^{2}}=\sqrt{8400^{2}+1700^{2}}=\sqrt{70560000 + 2890000}=\sqrt{73450000}\approx8570$ m.

Answer:

8570 m