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Answer :
Final answer:
Using the Pythagorean theorem, the magnitude of the vector sum of 25.0 m north and 18.0 m east is approximately 30.8 meters.
Explanation:
The vector sum of two vectors is calculated by first finding the resultant magnitude using the Pythagorean Theorem. This is a mathematical principle that is used to find the magnitude (length) of the resultant vector when two vectors at a right angle (90 degrees, like north and east) are added together.
These vectors are 25.0 m north and 18.0 m east, represented as a right triangle with the north as one side, the east as the other side, and the resultant vector as the hypotenuse. Therefore, the magnitude of the vector sum can be found by taking the square root of the sum of the squares of these two vectors:
Resultant Magnitude = sqrt[(25.0 m)^2 + (18.0 m)^2]
So, the magnitude of the vector sum is approximately 30.8 m.
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