Starting from one shore, you row a boat across a narrow river to the other shore. The river is 35.0 m wide. As you row, the river current causes your boat to move down the river a distance of 45.0 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 as a vector problem where the boat moves across the river (one vector) and is also displaced downstream by the river current (another vector).

Given dataTo determine the resultant displacement of the boat, we can treat this as a vector problem where the boat moves across the river (one vector) and is also displaced downstream by the river current (another vector).

Given 
- Distance across the river (perpendicular to the current) = 35.0 m
- Distance downstream due to the current (parallel to the river) = 45.0 m

We can consider these distances as the legs of a right triangle, and the resultant displacement will be the hypotenuse. Using the Pythagorean theorem:

\[
\text{Resultant displacement} = \sqrt{(\text{Distance across the river})^2 + (\text{Distance downstream})^2}
\]

Substituting the values:

\[
\text{Resultant displacement} = \sqrt{(35.0)^2 + (45.0)^2}
\]

\[
\text{Resultant displacement} = \sqrt{1225 + 2025}
\]

\[
\text{Resultant displacement} = \sqrt{3250}
\]

\[
\text{Resultant displacement} \approx 57.0 \, \text{m}
\]

Thus, the magnitude of the boat's resultant displacement is approximately **57.0 meters**.

Would you like a further breakdown of the method, or any other details?

Here are 5 related questions:
1. How would the displacement change if the river current increased?
2. What would be the angle of the resultant displacement with respect to the riverbank?
3. How much time would it take to cross the river if your rowing speed was given?
4. If you want to travel straight across without being pushed downstream, how would you adjust your rowing direction?
5. How would the result change if the river was 50.0 m wide instead of 35.0 m?

**Tip:** When dealing with displacement vectors, always break the motion into perpendicular components and use the Pythagorean theorem for resultant magnitudes.

Starting from one shore, you row a boat across a narrow river to the other shore. The river is 35.0 m wide. As you row, the river current causes your boat to move down the river a distance of 45.0 m. What is the resultant displacement of your boat? Determine the magnitude of the displacement.

Learn how to calculate the resultant displacement of a boat crossing a 35.0 m wide river while being displaced downstream by 45.0 m. This solution uses vector addition and the Pythagorean Theorem. Suitable for students in Grades 9-12.

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