a helicopter lifts a 72kg astronuat 15m vertically from the ocean by means of a cable. the acceleration of the astronuat is 9/10. how much work is done on the astronuat by; a)the force from the helicopter and b) the gravitational force on her? just before she reaches the helicopter, what are her c) kinetic energy and speed?

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To calculate the work done on the astronaut by the force from the helicopter and the gravitational force, we'll need to use the work-energy principle. The work done on an object is equal to the change in its energy.

a) Work done by the force from the helicopter:
Work is defined as the product of force and displacement. In this case, the force from the helicopter is equal to the weight of the astronaut, which is given by the equation F = mg, where m is the mass of the astronaut (72 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, the force from the helicopter is F_helicopter = 72 kg * 9.8 m/s^2.

The displacement is the vertical distance the astronaut is lifted, which is given as 15 m.

The work done by the helicopter can be calculated using the formula:
Work_helicopter = Force_helicopter * Displacement
Work_helicopter = F_helicopter * 15 m

b) Work done by the gravitational force:
Since the astronaut is lifted vertically and the gravitational force acts vertically downwards, the work done by the gravitational force will be negative as it is in the opposite direction of the displacement.

The work done by gravitational force can be calculated using the formula:
Work_gravity = - (Force_gravity * Displacement)
Work_gravity = - (F_gravity * 15 m)

To calculate the gravitational force, we need to multiply the mass of the astronaut (72 kg) by the acceleration due to gravity (9.8 m/s^2).
F_gravity = 72 kg * 9.8 m/s^2

c) Just before reaching the helicopter, the astronaut will have potential energy, which can be converted into kinetic energy. The total mechanical energy (E) is the sum of potential energy (U) and the kinetic energy (K):
E = U + K

Potential energy at the top of the lift (U) can be calculated using the equation:
U = m * g * h
U = 72 kg * 9.8 m/s^2 * 15 m

Now, to find the kinetic energy (K), we can use the equation:
K = E - U

Let's calculate the values:

a) Work done by the force from the helicopter:
Work_helicopter = F_helicopter * Displacement

b) Work done by the gravitational force:
Work_gravity = - (F_gravity * Displacement)

c) Just before reaching the helicopter:
Potential energy (U) = m * g * h
Kinetic energy (K) = E - U

Now, you can substitute the given values and solve for each part.