A mountain-climbing expedition establishes two intermediate camps, labeled A and B in the drawing, above the base camp. (x1 = 10500 m, and x2 = 17500 m.) What is the magnitude Är of the displacement between camp A and camp B?
To find the magnitude of the displacement between camp A and camp B, we can use the formula for displacement:
Δr = √[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]
Given that we are only interested in the magnitude of the displacement, we can ignore the y and z components for now and focus on the x-components.
Here, x1 represents the position of camp A, which is 10500 m, and x2 represents the position of camp B, which is 17500 m.
So, the displacement in the x-direction is:
Δx = x2 - x1
= 17500 m - 10500 m
= 7000 m
Now, we can calculate the magnitude of the displacement by substituting the Δx value into the displacement formula:
Δr = √[(Δx)^2 + (Δy)^2 + (Δz)^2]
Since we are only interested in the x-component of the displacement, the Δy and Δz values will be zero.
Thus, the magnitude of the displacement between camp A and camp B is:
Δr = √[(7000 m)^2 + (0)^2 + (0)^2]
= √[(7000 m)^2]
= 7000 m
Therefore, the magnitude of the displacement between camp A and camp B is 7000 meters.