Physics Help (Forces and Trigonometry)

Question

Two tugboats pull a larger boat with forces of 25000 N on each tow rope. What is the resultant force on the ship of the angle between the two ropes is 40°?

Answer 1

Solution:

You have to realize that since the forces are equal force vectors, the resultant force is also a vector that bisects the angle between the two tug boat ropes. If you complete the parallelogram, you get two similar triangles each with two 20 degree angles and one central 140 degree angle for a sum of 180 degrees and by using the law of cosines

R = √[( 25,000 N)²+(25000 N)² - 2( 25,000 N)( 25,000 N) cos (°140°)] = 46990 N OR approximately 47 kN

Lets just assume that the forces are perpendicular to each other then

R = √[(Fx)²+(Fy)² - 2(Fx)(Fy) cos ( 90°)] , but cos (90°) is zero so the equation is reduced to

R = √(Fx)²+ (Fy)² for forces perpendicular to each other in which R is the hypotenuse of a right angle triangle with equal sides