A person ran 160 meters east and then 175 meters north. Find the total distance covered by the person.
Before starting this question, we recall our four main compass points, north, east, south, and west, as shown. In this question, we’re interested in east and north. If we consider point 𝑂 to be the origin, the person originally runs 160 meters east. They then run 175 meters north. As we are asked to find the total distance covered, we need to add 160 and 175. This is equal to 335. The total distance covered by the person is 335 meters.
Had we been asked to calculate the displacement instead of the distance covered, we would be looking for the change in position from the origin. This would be the straight line distance 𝑥. We can calculate this length or distance by using the Pythagorean theorem. This states that the square of the hypotenuse is equal to the sum of the squares of the two shorter sides. 𝑥 squared is equal to 160 squared plus 175 squared. This means that 𝑥 squared is equal to 56225. Square rooting both sides of this equation gives us 𝑥 is equal to 237.12, to two decimal places.
The displacement of the runner after having run 160 meters east and 175 meters north is 237.12 meters. This is their distance from the origin.