The magnitude of the hiker's resultant displacement after walking 3 km north, 4 km east, and 6 km south is 5 kilometers, calculated using Pythagoras' theorem on a right-angled triangle formed by the net north-south and east-west movement.
To determine the magnitude of the resultant displacement of a hiker who walks 3 km north, 4 km east, and 6 km south, we can use vector addition. The hiker's initial displacement north is partially canceled out by the displacement to the south. Viewing this as a right-angled triangle where the legs represent the total north-south and east-west displacement, we have one leg of 3 km north minus 6 km south, resulting in a net movement of 3 km south, and the other leg remains at 4 km east.
To find the magnitude of the resultant displacement, we use Pythagoras' theorem. The magnitude is the hypotenuse of the triangle, calculated as:
\(\sqrt{(3 km)^2 + (4 km)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 km\)
In conclusion, the magnitude of the hiker's resultant displacement is 5 kilometers.