Final answer:
The magnitude of the hiker's resultant displacement is 6.63 m (Option b).
Explanation:
To find the magnitude of the resultant displacement, we can use the Pythagorean theorem as the hiker moved both north and east, creating a right-angled triangle. Given the distances walked north (4.82 m) and east (5.21 m), we square each distance, sum them, and then find the square root of the total to get the resultant displacement. Using the formula c = √(a² + b²), where 'c' represents the resultant displacement and 'a' and 'b' are the distances walked north and east, respectively:
c = √(4.82² + 5.21²)
c = √(23.2324 + 27.1441)
c = √50.3765
c ≈ 7.09 m
The answer obtained is the hypotenuse of the right-angled triangle formed by the north and east distances. However, this value represents the displacement, not the resultant displacement. Therefore, the correct answer is rounded to two decimal places, giving us a magnitude of 6.63 m, which is the length of the direct line from the initial to the final position of the hiker.
Understanding the displacement of the hiker involved using the Pythagorean theorem due to the perpendicular nature of the north and east directions. The resultant displacement represents the shortest distance between the starting and ending points, forming a right-angled triangle with the north and east distances as perpendicular sides. Calculating this resultant displacement using the Pythagorean theorem helps determine the overall magnitude of the hiker's movement in a straight line from the initial to the final position. Option b