00:01
Hi there, so for this problem, we have the situation that is shown in this figure.
00:04
Let's label this as the force f1 and the force f2.
00:08
Now we are given their magnitudes and their direction in good respect to the positive axis, okay? we need to find the direction and magnitude of the resultant force.
00:21
Now we know that the resultant force f is just the sum of the force f1 plus the force f2.
00:28
Now let's write those two.
00:31
So for the force f1, we know that that is its magnitude.
00:35
Then since the angle is given with respect to the horizontal, the x component is given by the cosine of 30 degrees, okay? this in the x direction.
00:48
Now for the y direction, it is positive because it is upward and that will be the sine of 30 degrees.
00:56
Now for the force f2, that will be then the magnitude that is 400.
01:01
Now in this case, while the x direction is positive and it is given with respect to the positive x axis as well, so that will be positive because it's to the same direction to the right.
01:17
And we set that to be positive, but the y direction is negative because it is downward.
01:22
So that will be minus the sine of 45 degrees in the y direction.
01:33
Now, once we have this, we can simplify this.
01:36
So then this force will be then 600 times the cosine of 30 degrees.
01:42
This plus 400 times the cosine of 45 degrees.
01:48
This will give us approximately 802 .46 in the x direction...