A man pushes a lawn mower with a force of 26 lb exerted at an angle of 30 degrees to the ground.Find the horizontal and vertical components of the force.

Answer 1

Sure thing.

Think of this just like a triangle. Our hypotenuse of the triangle is 26 lb since that is the full force of the push. We are at an angle of 30 degrees.

So, we know that cosine of our angle (30 degrees) is equal to the adjacent over the hypotenuse. Thus, cos(30) = adj / 26. The adjacent angle is the same as our x component, or the horizontal component. So, to find x, multiply 26 on both sides to get 26*cos(30) which equals 22.5

We know that sine of our angle (30 degrees) is equal to the opposite over the hypotenuse. Thus, sin(30) = opp / 26. The opposite angle is the same as our y component, or the vertical component. So, to find y, multiply 26 on both sides to get 26*sin(30) which equals 13.