starting from one shore, you row a boat across a narrow river to the shore on the other side. the river is a 35.0 m wide. as you row, the river current causes your boat to move down the river a distance of 50.0 m. what is the resultant displacement of your boat? determine the magnitude of the displacement.

To determine the resultant displacement of the boat, we can treat this situation as a right-angled triangle problem. The width of the river and the downstream distance traveled due to the current form the two legs of the triangle, and the resultant displacement is the hypotenuse.

### Given:
- Width of the river (horizontal leg) = \( 35.0 \, \text{m} \)
- Downstream distance (vertical leg) = \( 50.0 \, \text{m} \)

### Applying the Pythagorean Theorem:
\[
\text{Resultant displacement}^2 = (\text{width of the river})^2 + (\text{downstream distance})^2
\]
\[
d^2 = 35.0^2 + 50.0^2
\]
\[
d^2 = 1225 + 2500
\]
\[
d^2 = 3725
\]
\[
d = \sqrt{3725}
\]
\[
d \approx 61.06 \, \text{m}
\]

### Result:
The magnitude of the resultant displacement of your boat is approximately **61.06 meters**.

Would you like to know more details, or have any questions?

Here are five related questions:
1. What would happen to the resultant displacement if the current was stronger and caused the boat to drift 60 m downstream?
2. How would the angle of the boat’s path change if the downstream distance increased?
3. What is the angle between the boat's resultant displacement and the shore?
4. How would you calculate the time taken to cross the river if you knew the rowing speed?
5. What would the resultant displacement be if the river were twice as wide?

**Tip**: To find the direction of the boat’s displacement, you can use trigonometric ratios like tangent to calculate the angle.

Learn how to calculate the resultant displacement of a boat crossing a 35.0 m wide river while being carried 50.0 m downstream by the current. This problem demonstrates the use of the Pythagorean theorem and is suitable for students in Grades 8-10.

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