In diving to a depth of 785 m, an elephant seal also moves 410 m due east of his starting point. What is the magnitude of the seal's displacement?
To find the magnitude of the seal's displacement, we can use the Pythagorean theorem. Let's break down the problem into its components:
1. The diving depth: The seal dives down to a depth of 785 m. Since this is vertical movement, it does not affect the horizontal displacement. We can ignore this for now.
2. The eastward movement: The seal moves 410 m due east. This acts as the horizontal displacement.
Now, we can calculate the magnitude of the seal's displacement as follows:
1. Square the eastward displacement: (410 m)^2 = 168,100 m^2.
2. Square the diving depth (though we don't need it for this question): (785 m)^2 = 616,225 m^2.
3. Find the sum of the squared displacements: 168,100 m^2 + 616,225 m^2 = 784,325 m^2.
4. Take the square root of the result to find the magnitude of the displacement: √(784,325 m^2) = 885.50 m.
Therefore, the magnitude of the seal's displacement is approximately 885.50 meters.
To find the magnitude of the displacement, we need to find the straight-line distance between the starting point and the final position of the seal. This can be found using the Pythagorean theorem.
According to the given information, the elephant seal moves 410 m due east, and it also dives to a depth of 785 m. These two distances form two sides of a right triangle, with the magnitude of the displacement being the hypotenuse.
Using the Pythagorean theorem, we have:
Displacement^2 = (distance moved east)^2 + (distance dived)^2
Displacement^2 = 410^2 + 785^2
Displacement^2 = 168100 + 616225
Displacement^2 = 784325
Taking the square root of both sides, we have:
Displacement = √784325
Displacement ≈ 885.68 m
Therefore, the magnitude of the seal's displacement is approximately 885.68 m.