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The problem describes a situation where a person rows a canoe across a river 45.0 m wide. The resultant displacement (diagonal distance traveled) is given as 61.0 m. The goal is to find how far the river's current moved her downstream, which is the horizontal displacement along the river's width.

This can be solved using the Pythagorean theorem because the motion forms a right triangle, where:
- The width of the river (45.0 m) is one leg of the triangle.
- The resultant displacement (61.0 m) is the hypotenuse.
- The downstream distance (which we need to find) is the other leg.

According to the Pythagorean theorem:
\[
\text{(Downstream distance)}^2 + \text{(River width)}^2 = \text{(Resultant displacement)}^2
\]
Let \( d \) be the downstream distance. We can rearrange this to:
\[
d^2 = (\text{Resultant displacement})^2 - (\text{River width})^2
\]
\[
d^2 = 61.0^2 - 45.0^2
\]

Now, let's calculate this value.The downstream distance the current moved the canoe is approximately 41.2 meters. 

Thus, the correct answer is **C. 41.2 m**.

Would you like more details or have any questions? Here are some related questions to deepen understanding:

1. What would happen if the river's width were doubled while keeping the resultant displacement constant?
2. How could you calculate the current's velocity based on this downstream distance and the canoe's rowing speed?
3. Can you explain the relationship between vector components and this problem?
4. How does the Pythagorean theorem apply to situations involving two-dimensional motion?
5. How can we calculate the angle between the direction of the resultant displacement and the direct path across the river?

**Tip**: For motion problems involving perpendicular directions, always check if the Pythagorean theorem applies!

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?

Solve a canoe problem using the Pythagorean Theorem. A person rows across a 45 m wide river and measures a 61 m resultant displacement. Learn how to find how far the current moved her downstream.

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