Answer:
<em>A) it transforms a small force acting over a large distance into a large force acting over a small distance.</em>
Explanation:
The hydraulic lever works based on Pascal's law of transmission of pressure through a fluid. In the hydraulic lever, the pressure transmitted is the same.
Pressure transmitted P = F/A
where F is the force applied
and A is the area over which the force is applied.
This pressure can be manipulated on the input end as a small force applied over a small area, and then be transmitted to the output end as a large force over a large area.
F/A = f/a
where the left side of the equation is for the output, and the right side is for the input.
The volume of the displaced fluid will be the same on both ends of the hydraulic lever. Since we know that
volume V = (area A) x (distance d)
this means that the the piston on the input smaller area of the hydraulic lever will travel a greater distance, while the piston on the larger output area of the lever will travel a small distance.
From all these, we can see that the advantage of a hydraulic lever is that it transforms a small force acting over a large distance into a large force acting over a small distance.
We have the relation
where denotes the velocity of a body A relative to another body B; here I use B for boat, E for Earth, and R for river.
We're given speeds
Let's assume the river flows South-to-North, so that
and let be the angle made by the boat relative to East (i.e. -90° corresponds to due South, 0° to due East, and +90° to due North), so that
Then the velocity of the boat relative to the Earth is
The crossing is 153.0 m wide, so that for some time we have
which is minimized when so the crossing takes the minimum 30.0 s when the boat is pointing due East.
It follows that
The boat's position at time is
so that after 30.0 s, the boat's final position on the other side of the river is
and the boat would have traveled a total distance of