https://file.aiquickdraw.com/mathbot/file/1728680812820djlymsnc.jpg

The problem in the image describes a situation where a boat is rowed across a river that is 35.0 meters wide, but the river's current causes the boat to drift 45.0 meters downstream. To find the resultant displacement, we treat this as a right triangle problem, where the width of the river and the downstream distance form the two perpendicular sides of the triangle, and the resultant displacement is the hypotenuse.

We can use the Pythagorean theorem to find the resultant displacement (\(d\)):

\[
d = \sqrt{{(35.0 \, \text{m})^2 + (45.0 \, \text{m})^2}}
\]

Let's compute this:

\[
d = \sqrt{{(35.0)^2 + (45.0)^2}} = \sqrt{{1225 + 2025}} = \sqrt{3250} \approx 57.0 \, \text{m}
\]

Thus, the magnitude of the displacement is **57.0 meters**, which corresponds to option D.

Would you like further clarification on this, or have any questions? Here are 5 additional related questions to consider:

1. How would the resultant displacement change if the river were wider?
2. What would happen to the displacement if the current moved the boat less downstream?
3. Can the Pythagorean theorem be applied in situations other than geometry?
4. What factors could influence the boat’s trajectory in the real world?
5. How could the boat rower adjust their path to reduce the effect of the current?

**Tip:** When solving problems involving right triangles, remember to use the Pythagorean theorem when two sides are given, and you need to find the hypotenuse or the missing side.

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.

This problem involves finding the resultant displacement of a boat rowed across a 35.0 m wide river, where the boat drifts 45.0 m downstream. Using the Pythagorean theorem, learn how to compute the displacement step by step.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation