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?

jamesj · Answer

Start with a diagram and resolve forces.  All the boats here are headed east, let's say, and make that the direction of your x-axis.

Then find the x-component of the two forces T1 and T2.  The sum of x components must equal the drag of 4000 N.  Further, the y-components of the two forces must be equal and opposite, hence in magnitude T1 = T2.

Given all that, this should be pretty straight-forward.