Vector in a Plane

[rinspd]

The figure below illustrates two tugboats pulling a barge. If tugboat
A exerts a force of 5000 pounds, what force must tugboat B
exert if the barge is to move along the straight line l?

Here is what I have so far: let f be the magnitude of tugboat B
tugboat A: 5000<cos40,sin40>
tugboat B: f<cos35,sin35>
5000<cos40,sin40> = f<cos35,sin35>
5000cos40=f(cos35)
f=4676 lbs

I am not sure this is the right way to solve this problem?

 

[Deleted member 4993]

The figure below illustrates two tugboats pulling a barge. If tugboat
A exerts a force of 5000 pounds, what force must tugboat B
exert if the barge is to move along the straight line l?
View attachment 2330
Here is what I have so far: let f be the magnitude of tugboat B
tugboat A: f1<cos40,sin40>
tugboat B:f2<cos35,sin35>
5000<cos40,sin40> = f<cos35,sin35>
5000cos40=f(cos35)
f=4676 lbs

I am not sure this is the right way to solve this problem?

That is not correct.

It should be:

f1<cos(40°),sin(40°)> + f2<cos(-35°),sin(-35°)> = 5000<cos 0°,sin 0°>

Where R is the resultant force vector.

then

f1*cos40° + f2 * cos35° = 5000

f1*sin40° - f2 * sin35° = 0

and continue.....

 

[HallsofIvy]

Your attempt assumes that the forces applied by the two tugboats are 5000 pounds. That is incorrect. It is the force applied by the barge that is 5000 pounds. Call the two forces, applied by the two tugboats, T1 and T2. Then the horizontal components of the forces are T1 cos(40) and T2 cos(35) and that is what is pulling the barge. The vertical components are T1 sin(40) (upward) and T2 sin(35) (downward) and, since the barge is continuing horizontally, those must cancel: you have T1 cos(40)+ T2cos(35)= 5000 and T1 sin(40)= T2 sin(35). Solve those two equations for T1 and T2.