Final answer:
By applying the Pythagorean theorem to the eastward and southward components of Tremaine's jog, we find that the magnitude of his displacement is approximately 55.46 meters, which is closest to the provided option D, 60 meters.
Step-by-step explanation:
The student asked to find the magnitude of Tremaine's displacement after he jogged 24 meters east to the store and then 50 meters south to the mall. To determine the displacement, we can use the Pythagorean theorem since displacement is the shortest (straight-line) distance from the starting point to the ending point in vector terms. Displacement is a vector quantity that considers both magnitude and direction.
In this case, we can consider Tremaine's jog as two sides of a right-angled triangle, with the displacement being the hypotenuse. We can calculate this using the equation:
Displacement2 = East2 + South2
So:
Displacement2 = 242 + 502
This results in:
Displacement2 = 576 + 2500 = 3076
Taking the square root of 3076 gives us the magnitude of the displacement:
Displacement = √3076 ≈ 55.46 meters
Hence, from the given options, the magnitude of his displacement is closest to option D, 60 meters.