How would I solve this?

Question

"Two crewmen pull a boat through a lock, as shown in Figure 5-22. One crewman pulls with a force of F1 = 120 N at an angle of θ = 34° relative to the forward direction of the boat. The second crewman, on the opposite side of the lock, pulls at an angle of 45°. With what force F2 should the second crewman pull so that the net force of the two crewmen is in the forward direction?"

 

I used cos(34)=a/120 to find the middle line, (99.48) then cos(45)=99.48/h to find the hypoteneuse. I got 140.69, which isn't right. What am I doing wrong?

Answer 1

You want the net force to be only in the forward direction.  Therefore, the components of the 2 forces perpendicular to the forward direction must cancel.  That means

 

F₁sin34º = F₂sin45° ⇒

 

F₂ = F₁sin34º/sin45° = (120 N)sin34º/sin45° ≅ 94.90 N