Question

A mountain-climbing expedition establishes two intermediate camps, labeled A and B in the drawing, above the base camp. (x1 = 10000 m, and x2 = 18000 m.) What is the magnitude Δr of the displacement between camp A and camp B?

Answer 1

Answer on Question #46592-Physics-Mechanics-Kinematics-Dynamics

A mountain-climbing expedition establishes two intermediate camps, labeled A and B in the drawing, above the base camp. $\{x_{1} = 10000m$ , and $x_{2} = 18000m$ . What is the magnitude $\Delta r$ of the displacement between camp A and camp B?

Solution

The displacement is given by $\overline{\Delta r} = (\Delta x, \Delta y)$ where $\Delta x$ is difference in the $x$ positions of the camps and $\Delta y$ is the difference in the $y$ positions of the camps.

$$\Delta x = x _ {2} - x _ {1} = 1 8 0 0 0 - 1 0 0 0 0 = 8 0 0 0 m,$$ $$\Delta y = y _ {2} - y _ {1} = 4 9 0 0 - 3 2 0 0 = 1 7 0 0 m.$$

So $\overline{\Delta r} = (8000; 1700)$ m.

The magnitude $\Delta r$ of the displacement between camp A and camp B is

$$\Delta r = | \overline {{\Delta r}} | = \sqrt {8 0 0 0 ^ {2} + 1 7 0 0 ^ {2}} = 8 1 7 9 m.$$

Answer: 8179 m.

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