Question

A vector has an x-component of -309 m, and a y- component of 187m.
Find the magnitude of the vector [?]m

Answer 1

To find the magnitude of a vector given its components, you can use the Pythagorean theorem. In a two-dimensional plane, the magnitude \( |\mathbf{v}| \) of a vector \(\mathbf{v}\) with components \(v_x\) (x-component) and \(v_y\) (y-component) is given by:

\[ |\mathbf{v}| = \sqrt{v_x^2 + v_y^2} \]

Given:
- \( v_x = -309 \) m
- \( v_y = 187 \) m

Plug these values into the formula:

\[ |\mathbf{v}| = \sqrt{(-309)^2 + (187)^2} \]

First, calculate \( (-309)^2 \) and \( (187)^2 \):

\[ (-309)^2 = 95481 \]

\[ (187)^2 = 34969 \]

Now, add these results together:

\[ 95481 + 34969 = 130450 \]

Finally, take the square root of the sum:

\[ |\mathbf{v}| = \sqrt{130450} \approx 361.11 \]

So, the magnitude of the vector is approximately \( 361.11 \) meters.