Final answer:
The total displacement of the student who walks 1.0 mile west and 1.8 miles north is calculated using the Pythagorean theorem and is approximately 2.06 miles, which is not one of the provided options.
Step-by-step explanation:
The question asks about calculating the total displacement of a student who walks 1.0 mile west and then 1.8 miles north. Displacement is a vector quantity that represents the shortest distance between the initial and final positions and is directed from the starting point to the final position. To solve this, we can use the Pythagorean theorem since the student's path creates a right triangle, with the legs being the distances walked west and north.
We calculate the hypotenuse of the triangle that represents the displacement vector. The calculation is as follows:
- Let the distance walked west be 'a' = 1.0 mi
- Let the distance walked north be 'b' = 1.8 mi
- Then the displacement 'd' = √(a² + b²)
- 'd' = √(1.0² + 1.8²)
- 'd' = √(1 + 3.24)
- 'd' = √4.24
- 'd' ≈ 2.06 mi
Thus, the total displacement of the student is approximately 2.06 miles. Please note that this option is not listed in the provided choices, indicating that there may have been a misprint in the question or options given. The closest option is 3) 1.9 mi, but to provide the most accurate answer based on calculations, it's approximately 2.06 miles.