A student walks 16 km west and then 9.1 km south. After that, the student walks 9.8 km west. Using vector addition, the magnitude of the student's displacement is

Question

BlackTom AI · Accepted Answer

Vector components: the total westward displacement is 16.0 km + 9.8 km = 25.8 km; the southward displacement is 9.1 km. These are perpendicular components of the net displacement vector, so use the Pythagorean theorem to find the magnitude.

Step-by-step reasoning and calculation:
1. Identify components:
   - x (west) = 16.0 + 9.8 = 25.8 km
   - y (south) = 9.1 km
2. Square each component:
   - x^2 = (25.8)^2 = 25.8 × 25.8 = 665.64
   - y^2 = (9.1)^2 = 9.1 × 9.1 = 82.81
3. Sum the squares:
   - x^2 + y^2 = 665.64 + 82.81 = 748.45
4. Take the square root to get the magnitude:
   - magnitude = sqrt(748.45) ≈ 27.36 km (rounded to two decimal places)

Why this is correct:
- Displacement is a vector; components along perpendicular directions add separately. The magnitude of the resultant is the square root of the sum of squared orthogonal components (Pythagorean theorem). Using the correct component sums (west components added, south component alone) gives the value computed above.

Why the other multiple-choice options are incorrect:
- 34.90 km: this is the total path length (16 + 9.1 + 9.8) rather than the straight-line displacement; it ignores vector direction.
- 15.30 km: does not match any correct combination of perpendicular component sums for these steps and arises from an incorrect algebraic manipulation.
- 11.01 km: equals sqrt((16 − 9.8)^2 + 9.1^2) and would correspond to subtracting 9.8 in the wrong direction (as if it were east), so it is based on an incorrect sign for the westward steps.

Conclusion: The correct magnitude of the student's displacement is 27.36 km, matching the provided answer.

A student walks 16 km west and then 9.1 km south. After that, the student walks 9.8 km west. Using vector addition, the magnitude of the student's displacement isNumerical

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