Question

The three vectors in the drawing have magnitudes of A = 4.95 m, B = 4.90 m, and C = 4.10 m. Find the resultant of the 3 vectors by the component method. Express the angle as an angle above or below the + or - x-axis (Assume α = 23° / β = 52° )?

Answer 1

`(13.0, +66.8^circ)`

Explanation:

We need to break all of the vectors into their horizontal and vertical components. Because we don't have the drawing to follow, I am going to assume that it looks like this:

Therefore, we can calculate the horizontal component of their sum as
`|A| + cos( alpha) |B| + cos( beta) |C|`
`= 4.95"m" + 0.92 * 4.90"m" + 0.62 * 4.10"m" = 11.98`

We can now calculate the vertical component of their sum
`sin( alpha) |B| + sin( beta) |C| = 5.15`

Therefore, we have a final vector with magnitude
`|A+B+C| = sqrt(11.98^2 + 5.15^2) = 13.0`
and angle
`angle (A+B+C) = arctan(11.98/5.15) = 66.8^circ`

If the picture is different, I hope this at least gives an outline of what you're supposed to do.