A boy walking to school walks 3 km north and then 4 km west. The magnitude of his displacement is

Question

BlackTom AI · Accepted Answer

Consider the boy's path as perpendicular components: 3 km north and 4 km west. The resultant displacement is the vector sum of these two perpendicular legs.
Option a: 5 km. This matches the Pythagorean calculation sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 km, which is the correct magnitude.
Option b: 1 km. This would imply either subtracting or misplacing the components and does not reflect the true diagonal distance between start and end points; the components are perpendicular, so the displacement cannot be this small.
Option c: 7 km. This is the sum of the absolute values 3 + 4, but displacement is the straight-line distance, not the path length traveled; adding components directly ignores the right-angle geometry, so this is incorrect.
Option d: 5 km N53°W. Here the magnitude is correct, but the direction is misrepresented for a simple north-west displacement without a specified angle; the angle N53°W would correspond to a 53-degree angle from north toward west, which is not needed when stating just the magnitude, and mixing a directional form with a pure magnitude can be misleading in this context.
Overall, the right approach uses the Pythagorean theorem for perpendicular components, yielding a displacement magnitude of 5 km, while the other options either misuse the geometry or mix magnitude and direction inappropriately.

A boy walking to school walks 3 km north and then 4 km west. The magnitude of his displacement is

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