 In diving to a depth of 750 m, an elephant seal also moves 460 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 treat the movement as a right triangle, where the vertical movement (depth) and the horizontal movement (due east) are the two legs of the triangle. The displacement is the hypotenuse of this triangle.

### Given:
- Vertical movement (depth) = 750 meters
- Horizontal movement (due east) = 460 meters

We can use the Pythagorean theorem to find the magnitude of the displacement:

\[
\text{Displacement} = \sqrt{(\text{depth})^2 + (\text{east movement})^2}
\]

Substituting the given values:

\[
\text{Displacement} = \sqrt{(750)^2 + (460)^2}
\]

\[
\text{Displacement} = \sqrt{562,500 + 211,600}
\]

\[
\text{Displacement} = \sqrt{774,100}
\]

\[
\text{Displacement} \approx 880.93 \text{ meters}
\]

So, the magnitude of the seal's displacement is approximately **880.93 meters**.

Would you like more details or have any questions about this? Here are some related questions:

1. How would the displacement change if the seal moved 500 meters due east instead of 460 meters?
2. What is the significance of using the Pythagorean theorem in this context?
3. If the seal also moved 200 meters south, how would you calculate the new displacement?
4. What is the difference between displacement and distance traveled?
5. Can displacement ever be greater than the total distance traveled?

**Tip:** Displacement is a vector quantity, meaning it has both magnitude and direction, unlike distance, which is only a scalar quantity.

Learn how to calculate the magnitude of displacement when an elephant seal dives to a depth of 750 meters and moves 460 meters east. The displacement is found using the Pythagorean theorem. Suitable for high school students studying vectors and displacement.

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