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

We’re given a boy’s path: 3 km north followed by 4 km west. To find the displacement magnitude, focus on the straight-line distance from start to end, not the path traveled. The two legs form a right-angled triangle, with the northward leg as one side and the westward leg as the other.

Apply the Pythagorean theorem: displacement magnitude = sqrt((3 km)^2 + (4 km)^2) = sqrt(9 + 16) = sqrt(25) = 5 km.

This relies on the idea that displacement depends on initial and final positions, not the route taken, and that perpendicular directions combine via the Pythagorean relation for a right triangle.

If one were to consider the problem verbally, a 3-4-5 triangle immediately suggests a 5 km resultant displacement, since the two orthogonal displacements form the legs of a right triangle.

Note that the direction (north then west) only affects the orientation of the displacement vector; its magnitude remains determined by the square root of the sum of the squares of the components, as demonstrated. Any statement that the magnitude would be something other than 5 km would be inconsistent with the right-triangle relationship here.

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

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