Honors pre calc

Question

Determine the work done by a force F of 42 lbs acting in the direction 81° to the horizontal in moving an object 9 ft up an incline that forms a 15° angle to the horizontal. Round your answer to the nearest hundredth and use the unit of ft-lb. 

Answer 1

The work done is Fd sin θ where F is the force applied, d is the displacement and θ is the angle between the direction of the force and the direction of the displacement. Here the displacement is along the incline at an angle of 15º to the horizontal. The force is at an angle of 81° to the horizontal. So the angle between F and d is 81-15=66°

So, the work done = 42×9×cos(66)=153.75 ft-lb