Two forces of magnitudes 35 newtons and 91 newtons are acting at a particle. Given that the resultant is perpendicular to the first force, find the magnitude of the resultant.
So in this question, what we have is a particle. Remember, we have two forces that are acting on our particle. The first one of these is 35 newtons. Then before I draw the second force, what I’ve in fact done is I’ve drawn our resultant. And that’s because we’re told the resultant is perpendicular to this first force. So perpendicular means at right angles. So I’ve drawn in blue our resultant. And then, next, what I’ve done is I’ve drawn the second force. And this is 91 newtons.
Well, now what we can see we’ve got here is a right-angled triangle. So we’ve got our right angle, and we’ve got our hypotenuse, which is 91. And then we’ve got one of our short sides, which is 35. And then we have our resultant, and I’m gonna call our resultant 𝑅.
Well, because we’ve got a right-angled or right triangle, then what we can use is the Pythagorean theorem, because what we’re trying to do is find a missing side. And that tells us that 𝑎 squared plus 𝑏 squared is equal to 𝑐 squared, where 𝑐 is the longest side, the hypotenuse of our triangle.
Well, what you can do is rearrange the Pythagorean theorem if you’re trying to find one of the shorter sides. And what we get is 𝑎 squared. Well, in our case, this is 𝑅. So 𝑅 squared is equal to. Then you’ve got the hypotenuse squared, so 𝑐 squared, then minus the other side squared. So therefore, we’re gonna get 𝑅 squared is equal to 91 squared minus 35 squared. So therefore, what we’re gonna get is 𝑅 squared is equal to 8281 minus 1225. So therefore, 𝑅 squared is equal to 7056.
So therefore, if you want to find 𝑅, what we’re going to do is take the square root of both sides of the equation. And when we do that, we get 𝑅 is equal to 84. So we can say that the magnitude of the resultant is 84 newtons.