A person is pushing on a shopping cart with a force of 10 N at an angle of 35° with the horizontal. Find the x and y components (i.e. Fx and Fy) of this force.

Answer 1

Your sketch of the situation looks like this:

Using the triangle originating at the center of the shopping cart, you can write the sine and cosine ratios like this:

sin(35) = opposite/hypotenuse = F_y/10 or (multiplying both sides by 10

F_y = 10sin(35) = 5.736 N (I'll let you round to whatever sig figs your teacher expects)

and

cos(35) = adjacent/hypotenuse = F_x/10 or (multiplying both sides by 10

F_x = 10cos(35) = 8.192 N

Answer 2

X and Y components can be found using the sine and cosine functions.

Start by drawing a triangle with the magnitude of your force as the hypotenuse and one of the acute angles as the angle with the horizontal. The adjacent side is the x component of the force, and the opposite side is the y component.

Therefore, Fx = Fcosθ and Fy = Fsinθ, where F is the applied force.