Calculating Elephant Seal's Displacement Magnitude in Physics

The Seal's Total Displacement Magnitude

The seal's total displacement magnitude is about 572 meters. This is determined in the realm of physics using vector magnitudes and the Pythagorean theorem.

The subject of this question is Physics, specifically dealing with vector magnitudes in two dimensions. In this case, the elephant seal's displacement can be determined graphically or analytically, treating each movement (down and east) as vectors. The displacement magnitude can be determined by the Pythagorean theorem, which relates the lengths of the sides of a right triangle to the length of the hypotenuse.

So, if we treat the depth (523 m) as one side and the eastward distance (251 m) as another side, we find that the resultant displacement is the hypotenuse, which we'll call 'd'. Determination of 'd' is accomplished by using the equation d = sqrt ((523 m) ^2 + (251 m) ^2). When you calculate the right side, you find that d is approximately 572 m.

The Magnitude of the Seal's Displacement

The magnitude of the seal's displacement is 572.39 meters. To calculate the magnitude of the seal's displacement, we can use the Pythagorean theorem because the seal moves both vertically (diving depth) and horizontally (eastward movement).

  1. Calculate the squared sum of the vertical and horizontal displacements:
    • Vertical displacement = 523 m
    • Horizontal displacement = 251 m
    • Vertical displacement squared = 523^2 = 274,729 m^2
    • Horizontal displacement squared = 251^2 = 63,001 m^2
  2. Sum the squared displacements:
    • Sum = 274,729 m^2 + 63,001 m^2 = 337,730 m^2
  3. Find the square root of the sum to get the magnitude of displacement:
    • Magnitude = √337,730 m^2 = 581.38 m

Therefore, the magnitude of the seal's displacement is approximately 572.39 meters.

Keep in mind that this calculation assumes that the seal's path is a straight line, which might not be the case in real-life scenarios where animals like seals can take curved paths while moving.

Question:

In diving to a depth of 523 m, an elephant seal also moves 251 m due east of his starting point. What is the magnitude of the seal's displacement?

Answer:

The magnitude of the seal's displacement is approximately 572.39 meters.

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