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A helicopter lifts a 67 kg astronaut 11 m vertically from the ocean by means of a cable. The acceleration of the astronaut is [tex]\frac{g}{15}[/tex].

Answer :

Final answer:

The work done on the astronaut by the force from the helicopter is 147 N and by the gravitational force is 25.5 N. Just before reaching the helicopter, her kinetic energy is 0 and her speed is approximately 14.67 m/s.

Explanation:

To calculate the work done on the astronaut by the force from the helicopter, we can use the equation W = F * d, where W is the work, F is the force, and d is the distance.

In this case, the force from the helicopter is equal to the weight of the astronaut, which is given by F = m * g, where m is the mass of the astronaut and g is the acceleration due to gravity.

The distance is given as 11 m.

Plugging in the values, we have W = (67 kg * 9.8 m/s^2) * 11 m = 147 N.

To calculate the work done on the astronaut by the gravitational force, we can again use the equation W = F * d, where W is the work, F is the force, and d is the distance.

In this case, the force is the weight of the astronaut, which is given by F = m * g, and the distance is the vertical displacement of 11 m.

Plugging in the values, we have W = (67 kg * 9.8 m/s^2) * 11 m = 25.5 N.

Just before she reaches the helicopter, the astronaut's kinetic energy can be calculated using the equation K = 0.5 * m * v^2, where K is the kinetic energy, m is the mass, and v is the velocity.

Since the velocity is 0 (she is just about to reach the helicopter), the kinetic energy is 0.

Similarly, the speed can be calculated using the equation v = √(2 * g * h), where v is the velocity, g is the acceleration due to gravity, and h is the vertical displacement.

Plugging in the values, we have v = √(2 * 9.8 m/s^2 * 11 m) = √(214.8) ≈ 14.67 m/s.

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Complete Question:

A helicopter lifts a 67 kg astronaut 11 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/15. How much work is done on the astronaut 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 (d) speed?

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