Question

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

Explanation:

Step1: Find horizontal displacement

The horizontal distance from the base - camp to camp A is $x_A = 11200$ m and to camp B is $x_B=19600$ m. The horizontal displacement $\Delta x=x_B - x_A=19600 - 11200=8400$ m.

Step2: Find vertical displacement

The vertical distance of camp A from the base - camp is $y_A = 3200$ m and of camp B is $y_B = 4900$ m. The vertical displacement $\Delta y=y_B - y_A=4900 - 3200 = 1700$ m.

Step3: Use Pythagorean theorem

The magnitude of the displacement $\Delta r$ between camp A and camp B is given by $\Delta r=\sqrt{\Delta x^{2}+\Delta y^{2}}$. Substitute $\Delta x = 8400$ m and $\Delta y = 1700$ m into the formula: $\Delta r=\sqrt{(8400)^{2}+(1700)^{2}}=\sqrt{70560000 + 2890000}=\sqrt{73450000}\approx8570$ m.

Answer:

$8570$ m