Example 2: This example is a variant of the problem considered in Example 1. In this case, tugboat A is exerting a force of 15,000 N at 30° angle. We are interested in knowing the magnitude and direction of the force exerted by tugboat B on the cargo ship such that the resultant towing force is 30,000 N in the horizontal direction, as shown in the figure.

Solution: Having discussed, in previous example, various approaches to analyze a co-planar concurrent force system, we focus here on the scalar approach. The schematic drawing of the forces is shown below. The magnitude and direction of the force exerted by Tugboat A and those of the force resultant are known. The unknown quantities are the magnitude and direction of the force exerted by tugboat B.

The force equations in x and y directions are used to find the components of .

With the two components of force known, we can solve for its magnitude and direction as

Therefore, tugboat B should apply a force of 18,590 N at an angle of 24° below the x axis.