The summit of a mountain, 2082 m above base camp, is measured on a map to be 4582 m horizontally from the camp in a direction 32.4° west of north. Choose the x axis east, y axis north, and z axis up. What are the components of the displacement vector from camp to summit?
To find the components of the displacement vector from the camp to the summit, you can break it down into its x, y, and z components.
First, let's define the x-axis as east, the y-axis as north, and the z-axis as up.
Now, we can calculate the x, y, and z components separately.
The x-component represents the horizontal displacement from the camp to the summit, which is given as 4582 m. Since the displacement is measured west of north, we need to consider the angle of 32.4 degrees.
To find the x-component, we need to find the horizontal component of the displacement in the north direction. We can do this by calculating the north component multiplied by the cosine of the angle:
x-component = 4582 m * cos(32.4°)
Next, let's calculate the y-component, which represents the vertical displacement from the camp to the summit. The vertical displacement is given as 2082 m, which represents the height difference (z-component) between the camp and the summit. So the y-component is simply the z-component:
y-component = 2082 m
Therefore, the components of the displacement vector from the camp to the summit are:
x-component: 4582 m * cos(32.4°)
y-component: 2082 m
z-component: 0 m (since there is no vertical displacement)