Final answer:
To find the forces exerted by each tugboat, we resolve the forces into components and use trigonometry, considering that one tugboat pulls with twice the force of the other, and the resultant force is 400 kN north.
Step-by-step explanation:
The question involves resolving forces into their components and finding the resultant force on an object, which in this case is a disabled boat named Pequod being towed by two tugboats. We need to consider the given force of 400 kN north as the resultant force, apply trigonometry, and use the principle of superposition of forces to solve for the forces exerted by each tugboat.
To find the magnitude of force each tugboat exerts (a), let's assume the force exerted by the second tugboat is F. Since the first tugboat exerts twice this force, it would be 2F. The force exerted to the west of north by the first tugboat can be resolved into north and west components. The northward component of this force will add to the force of the second tugboat, and the westward component will cancel out as there is no westward resultant force given.
Using trigonometry, the northward component is 2F * cos(28.1°), and adding this to F (the force of the second tugboat), should equal 400 kN. From this equation, we can solve for F and consequently 2F. For (b) the direction for the second tugboat's force is directly north as the resultant force on the Pequod is perfectly north.