00:01
So with this question we're told that there's a force, 185 pound force acting on it, and there's another force with an angle of 78 degrees and 18 minutes, and it says that the resultant force is at 27 degrees and 4 minutes.
00:35
And we want to find the other force, let's call this v, so this would be the magnitude of v, and let's call this the resultant force here, so we're looking for the magnitude of r.
00:54
Well i'm going to do this, i'm going to actually take this drawing and i'm going to turn this sideways, so the resultant force is going like this.
01:04
So it's going to make it a little bit easier i think to look at this.
01:09
So that means that this angle right here is just going to be this 27 .4 degrees, 27, not .4, but 27 and 4 minutes is 4 60ths, right? so i'm going to write 4 60ths degrees, and then this angle right here is going to be the difference between these two angles, right? so 78 degrees and 18 minutes minus 27 degrees and 4 minutes is going to be 51 degrees and 12 minutes, or 51 and 12 60ths degrees, right? so what do we know? we know that this is 185, 185 pounds, this is going to be the magnitude of v, and this is going to be the magnitude of r, okay? so we're going to do this in two ways, we're going to write two equations, one is a horizontal equation and one is a vertical equation, okay? so i know that this magnitude, let me scroll down just a little bit to create more room, this magnitude of r is going to be equal to, since it's going directly to the right, that's my horizontal, that's going to be the cosines.
02:33
So this first one here, so this is going to be 185 cosine of this angle, 27 and 4 60ths degrees plus whatever the magnitude of v is times the cosine of that angle.
02:55
So 21, sorry, 51, 51 and 12 60ths degrees, right? well we also know that these two forces balance out because our resultant vector is directly horizontal because we've created it that way, right? so the vertical forces of the two cancel out, so they must be equal, right? well the vertical forces are going to be the sines.
03:25
So 185 degree or 185 pounds times the sine of 27 and 4 60ths degrees must equal, not plus, must equal the magnitude of v times the sine of that angle of 51 and 12 60ths degrees, right? well, in the second equation, i only have one variable, so i can go ahead and divide both sides by the sine of 51 and 12 60ths degrees...