‫Let's take another case now.
‫Again, you have the ball and the same force is acting on the ball diagonally at the angle of 30 degrees
‫and your ball travels along that diagonal, 20 meters like you see here.
‫The force applied was five Newtons diagonally.
‫And the absolute values here mean that it is the magnitude of the vector.
‫Remember, if you have a vector, let's say A and B and you want to compute its magnitude, then it
‫would be like this square root, A squared plus B squared.
‫And essentially this would be your A component.
‫This would be your B component.
‫And the Green Arrow here is the magnitude of this vector.
‫It's the length of this arrow.
‫Now, we can also write this force vector like this.
‫We can use the vector form.
‫And so the X component of this force would be five Newton's times cosine.
‫Thirty degrees.
‫Right.
‫You would get this component then and the Y component would be five times sine thirty degrees.
‫And so you would get this component then in the same thing with the displacement vector, the X component
‫would be 20 times cosine, 30 degrees in the Y component would be 20 times sine 30 degrees and the units
‫for the force vector would be Newton's and for the displacement vector meters.
‫So work here would be five times cosine.
‫Thirty degrees, which is the force X component times 20 times cosine, 30 degrees, which is this.
‫Plus I'm going to continue here five times sine thirty degrees, which is this one times.
‫Twenty times sine thirty degrees which is this one.
‫Then that means that you will get this.
‫The first term would be one hundred five times, 20 times cosine, 30 degrees squared plus again you
‫would have five times twenty.
‫So one hundred and sine thirty degrees squared you can factor out one hundred and inside the parentheses
‫you would have cosine 30 degrees squared plus sine thirty degrees squared.
‫And now there is a trigonometric identity that says that cosine alpha squared plus sine alpha squared
‫were both alphas are the same angles.
‫Right.
‫It's the same angle.
‫So when you have something like this then that will equal one.
‫And that's a very famous trigonometric identity.
‫And that means that here this thing here will be one.
‫So you are left with and I'm going to continue here.
‫You are left with one hundred, which is this one times one, which is this one here.
‫And so you have one hundred jewels of work done.
‫By this force, because only this force moved this ball from here to here over the distance of 20 meters.