Two tug boats are towing a large boat, of mass M kg, back to shore. Tug boat 1 is pulling with a force of T1 N at an angle of 25 degrees north of the forward motion and tug boat 2 is pulling with a force of T2 N at an angle of 25 degrees south of the forward motion. If the large boat is being pulled with constant velocity, and there is a resistive force of 4000N to the motion, then what are the magnitudes of the two forces T1 and T2?

Question

Two tug boats are towing a large boat, of mass M kg, back to shore.  Tug boat 1 is pulling with a force of T1 N at an angle of 25 degrees north of the forward motion and tug boat 2 is pulling with a force of T2 N at an angle of 25 degrees south of the forward motion.  If the large boat is being pulled with constant velocity, and there is a resistive force of 4000N to the motion, then what are the magnitudes of the two forces T1 and T2?

mathmate · Answer

Large boat has constant velocity, so only resistive force is F=4000N
It will be assumed that the large boat has a net velocity due east (since tug boats are symmetrically placed north and south).
Then sum forces N-S, or Fy:
Sum Fy=0 => T1sin(theta1)+T2sin(theta2)=0 => T1=T2
Sum Fx=0 => T1cos(theta1)+T2cos(theta2)=F 
Solve for T1 and T2.

anonymous · Answer

Please show steps! Im confused

mathmate · Answer

Can you start by drawing a diagram, this is the first step to solving the problem.

anonymous · Answer

Im on my phone right now, so I cant

mathmate · Answer

That's OK, take your time.
The best way to solve a physics (statics) problem is to visualize the problem in relation to its parameters.  This is most often done by a diagram indicating the object in question, forces acting on it, the direction, magnitude, and the notation you use.  Finally, you'd draw a free-body diagram and calculate forces by summing in each direction.