A child pulls a wagon along level ground by exerting a force

Question

A child pulls a wagon along level ground by exerting a force of 15 pounds on a handle that makes an angle of 30° with the horizontal, as shown in the figure. Find the work done in pulling the wagon 120 feet. (Round your answer to the nearest whole number.)

ft/lb= ?

Answer 1

Work = Force x Distance (measured in foot-lbs). The distance here is clearly 120 feet. So you need the force. If the force is exerted 30 degrees from horizontal, that force can be broken into two portions - that in the x-direction (what we need), and then in the y-direction. Since the proportions of the triangle are sqrt(3)/2, (x direction), 1/2 y direction, 1 (hypotenuse), multiply the force (15) x sqrt(3)/2.

Answer: 120*15*sqrt(3)/2 = 1558.85 ft-lbs (which rounds to 1559 ft-lbs)