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What is the resultant displacement of your boat? Determine the magnitude of the displacement.
A.35.0 m
B.61.0 m
C.85.0 m
D.1,225 m
E.2,500 m

The problem involves finding the resultant displacement of the boat, considering that the river current causes the boat to drift downstream as it crosses the river.

From the diagram:
- The width of the river (perpendicular distance) is \( 35.0 \, \text{m} \).
- The boat is moved downstream by the current by \( 50.0 \, \text{m} \) (parallel distance).

To find the resultant displacement (\( \Delta d_{\text{res}} \)), we treat this as a right triangle where the legs are the river width and the downstream distance, and the hypotenuse is the resultant displacement. We can use the Pythagorean theorem to calculate it:

\[
\Delta d_{\text{res}} = \sqrt{(35.0 \, \text{m})^2 + (50.0 \, \text{m})^2}
\]

Now, I'll calculate the magnitude.The magnitude of the resultant displacement of your boat is approximately \( 61.0 \, \text{m} \).

So, the correct answer is:
**B. 61.0 m**

Do you want more details or have any questions?

Here are 5 related questions:
1. How would the displacement change if the river's current caused a 60.0 m downstream drift?
2. What would the angle of displacement be with respect to the river bank?
3. How would you calculate the boat's velocity if it crosses the river in 10 seconds?
4. What impact does increasing the river width have on the resultant displacement?
5. How would the boat's path change if the river's current doubled?

**Tip:** The Pythagorean theorem is useful for calculating displacement in right-angled motion problems like this one!

What is the resultant displacement of your boat? Determine the magnitude of the displacement.
A. 35.0 m
B. 61.0 m
C. 85.0 m
D. 1,225 m
E. 2,500 m

Determine the magnitude of the resultant displacement of a boat crossing a 35.0 m wide river, drifting 50.0 m downstream. This problem demonstrates the application of the Pythagorean theorem to calculate the displacement in a right triangle. Suitable for Grades 9-12.

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