To find the magnitude of a vector given its components, we can use the Pythagorean theorem. The magnitude (or length) of a vector with components [tex]\((x, y)\)[/tex] is given by the formula:
[tex]\[ \text{Magnitude} = \sqrt{x^2 + y^2} \][/tex]
Here's a step-by-step breakdown:
1. Identify the components of the vector:
- The x-component [tex]\( x \)[/tex] is 15 meters.
- The y-component [tex]\( y \)[/tex] is 8 meters.
2. Square each component:
[tex]\[
x^2 = 15^2 = 225 \\
y^2 = 8^2 = 64
\][/tex]
3. Sum the squares of the components:
[tex]\[
x^2 + y^2 = 225 + 64 = 289
\][/tex]
4. Take the square root of the sum to find the magnitude:
[tex]\[
\text{Magnitude} = \sqrt{289} = 17 \, \text{meters}
\][/tex]
Therefore, the magnitude of the vector with components [tex]\((15 \, \text{m}, 8 \, \text{m})\)[/tex] is [tex]\( 17 \, \text{meters} \)[/tex].
