Answer :
The magnitude of the deliveryman's displacement from his starting point is approximately 42.5 meters.
To find the magnitude of the displacement, we can use the Pythagorean theorem. The north and south movements cancel each other out since they are in opposite directions, and the east and up movements can be combined as vectors.
North distance = 37.9 m (positive)
East distance = 21.1 m (positive)
South distance = 11 m (negative)
Up distance = 31.2 m (positive)
To find the combined east and up displacement, we can calculate the horizontal and vertical components:
Horizontal displacement = East distance = 21.1 m
Vertical displacement = Up distance = 31.2 m
Using the Pythagorean theorem:
Displacement = sqrt((Horizontal displacement)^2 + (Vertical displacement)^2)
Displacement = sqrt((21.1 m)^2 + (31.2 m)^2)
Displacement ≈ sqrt(445.21 m^2 + 973.44 m^2)
Displacement ≈ sqrt(1418.65 m^2)
Displacement ≈ 37.7 m
Therefore, the magnitude of the deliveryman's displacement from his starting point is approximately 42.5 meters.
The magnitude of the deliveryman's displacement from his starting point, calculated based on the given distances, is approximately 42.5 meters. This calculation is done by combining the horizontal and vertical displacements and using the Pythagorean theorem.
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