Answer :
The magnitude of a vector with an x-component of 15.8 m and a y-component of 36.9 m is approximately 40.13 meters, calculated using the Pythagorean theorem.
To find the magnitude of a vector given its x-component and y-component, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). Applying this to vector components, if a vector has an x-component of 15.8 m and a y-component of 36.9 m, the magnitude can be calculated as follows:
Magnitude =
√(x-component)² + (y-component)²
= √(15.8 m)² + (36.9 m)²
= √(249.64 m² + 1361.21 m²)
= √(1610.85 m²)
= 40.13 m
Therefore, the magnitude of the vector is approximately 40.13 meters.