Final answer:
The correct answer is that the output force on a riverboat's paddle wheel is greater than the input force and is exerted over a greater distance, similar to the mechanical advantage gained with a wheelbarrow.
Step-by-step explanation:
Regarding the question on a riverboat, which statement about the output force is true when the force of the engine is applied to the axle of a large paddle wheel, option 4 is the correct answer: the output force is greater than the input force and is exerted over a greater distance. This principle follows from the mechanical advantage provided by levers such as the wheel and axle. When a wheel and axle are used as in the case of a riverboat's paddle wheel, the output force on the paddle wheel’s circumference can be larger than the input force applied to the axle due to the larger radius of the wheel compared to the axle. Thus, while the engine applies a certain force to the axle, the resulting force on the outer edge of the paddle wheel can lift a considerably heavier load over a larger distance. This is like lifting a heavy load with a wheelbarrow, where the lever principle enables one to lift more than they could alone.