Final answer:
The magnitude of a vector with an x-component of 6.15m and a y-component of -3.88m is approximately 7.28m, calculated using the Pythagorean theorem.
Step-by-step explanation:
To find the magnitude of a vector with given x- and y-components, we use the Pythagorean theorem. The magnitude (often represented as |v| or v) of a vector with x- and y-components can be calculated using the equation |v| = √(x² + y²), where x and y are the components of the vector along the x-axis and y-axis, respectively.
In the given problem, the vector has an x-component of 6.15m and a y-component of -3.88m. Plugging these into the formula, we obtain |v| = √((6.15m)² + (-3.88m)²).
Calculating the square of each component, we get (6.15m)² = 37.8225m² and (-3.88m)² = 15.0544m². Adding these, we have 37.8225m² + 15.0544m² = 52.8769m².
Taking the square root of this sum gives |v| = √(52.8769m²) = 7.27m, which we can round to 7.28m to match the given options. Hence, the magnitude of the vector is approximately 7.28 m, making option A the correct answer.