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The problem describes a situation where a person rows across a river with a width of 45.0 m, and the resultant displacement is 61.0 m. We need to find out how far the current moved the canoe downstream.

This can be solved using the Pythagorean theorem, as the motion forms a right-angled triangle:
- One side is the width of the river (45.0 m).
- The hypotenuse is the resultant displacement (61.0 m).
- The other side is the distance the current moved the canoe, which we are trying to find.

Let \( x \) be the distance the current moved the canoe downstream.

Using the Pythagorean theorem:
\[
x^2 + 45.0^2 = 61.0^2
\]
\[
x^2 + 2025 = 3721
\]
\[
x^2 = 3721 - 2025
\]
\[
x^2 = 1696
\]
\[
x = \sqrt{1696} \approx 41.2 \, \text{m}
\]

Thus, the distance the current moved the canoe is approximately **41.2 m**, which corresponds to option **C**.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How can you apply the Pythagorean theorem to other motion problems involving two perpendicular directions?
2. What does the resultant displacement represent in vector problems?
3. How would the answer change if the river's width or resultant displacement were different?
4. Can you think of real-life situations where understanding vector displacement is important?
5. How would the current's speed affect the motion of the canoe?

**Tip:** Always remember that the Pythagorean theorem is helpful when dealing with perpendicular motions or components in physics.

A person rows a canoe across a river that is 45.0 m wide. Using the GPS on her phone, she determines the resultant displacement is 61.0 m. How far down the river did the current move her canoe?

Learn how to solve a problem involving a canoe crossing a 45.0 m wide river with a 61.0 m resultant displacement. This step-by-step solution explains how to apply the Pythagorean theorem to find the downstream distance moved by the current, suitable for students in Grades 8-10.

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