Final answer:
The work done on a 75 kg flood survivor lifted 16 m vertically by a helicopter is 11760 J, calculated as the product of gravitational force and the distance.
Step-by-step explanation:
A military helicopter lifts a 75 kg flood survivor 16 m vertically from the river by a rope.
If the acceleration of the survivor is g/10, the work done on the survivor by the force from the helicopter can be calculated using the work-energy principle, which states that the work done by the forces on an object results in a change in the kinetic energy of that object.
Here, we can also consider gravity, which will do work on the survivor as they are lifted.
To calculate the work done by the helicopter, we can ignore the kinetic energy change since the scenario doesn’t mention any change in velocity implying that lifting is done at a constant velocity. Therefore, the work done by the helicopter can be calculated by the equation: Work = Force × Distance.
The force exerted by the helicopter will be equal to the weight of the survivor plus the additional force required to provide the upward acceleration, which is a fraction of g.
However, since the question doesn't ask us to account for the extra force from acceleration, we will focus on the gravitational force component for the work done against gravity.
To find the gravitational force, we use the equation:
Force = mass × gravity (F = mg), which for a 75 kg survivor is approximately 75 kg × 9.8 m/s2 = 735 N.
The work done against gravity is this force over the distance of 16 m, so Work = 735 N × 16 m = 11760 J (joules).