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

We can solve this problem using the Pythagorean theorem, as the situation forms a right triangle.

### Given:
- Width of the river (perpendicular distance): \( 45.0 \, \text{m} \)
- Resultant displacement (hypotenuse): \( 61.0 \, \text{m} \)

We need to find how far down the river the current moved her canoe (horizontal displacement), which we'll call \( x \).

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

### Conclusion:
The current moved her canoe approximately **41.2 meters** downstream.

Would you like more details on the calculation or have any other questions? Here are some related questions to explore:

1. What angle did the canoe's resultant displacement make with the riverbank?
2. How would the displacement change if the river was narrower?
3. If the current speed increased, how would that affect the downstream displacement?
4. What if the person rowed faster—how would it affect the resultant displacement?
5. How can we calculate the speed of the current using time and distance?

**Tip**: The Pythagorean theorem is useful for any right-angled triangle when you know two sides and need to find the third.

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 problem involving the displacement of a canoe across a 45-meter wide river using the Pythagorean theorem. The problem involves calculating how far the current moved the canoe downstream with a resultant displacement of 61 meters. Suitable for students in Grades 9-10.

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