What is the resultant vector for the following?
Two vectors F1 and F2 where F1 = 34 N and F2= 65 N with F1 forming an angle of 240 degrees and F2 an angle of 25 degrees with the positive x-axis and a counter-clockwise rotation being considered positive.
The two vectors provided are F1 and F2 which have a magnitude of 34 N and 65 N resp. and which form an angle of 240 degrees and 25 degrees resp. with the positive x- axis.
Now we split the two vectors into their x and y components.
We see that F1x = -34* sin 30 and F1y = -34 * cos 30.
For the vector F2, F2x = 65 *cos 25 and F2y = 65*sin 25.
Let the resultant vector be denoted as F.
Fx = 65*cos 25 - 34*sin 30 = 41.91
Fy = 65*sin 25 - 34*cos 30 = -1.97
The magnitude of the resultant vector is sqrt (41.91^2 + 1.97^2)
=> 41.95 N
The direction of the resultant vector is arc tan ( 41.91/(-1.97)) = -87.3 degrees.
Therefore the required resultant vector of the given vectors has a magnitude of 41.95 N and an angle of -87.3 degrees to the positive x-axis.