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An airplane pilot fell 370$\mathrm { m }$ after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1$\mathrm { m }$ deep, but survived with only minor injuries. Assuming the pilot's mass was 88$\mathrm { kg }$ and his terminal velocity was 45$\mathrm { m } / \mathrm { s }$ , estimate: $( a )$ the work done by the snow in bringing him to rest; (b) the average force exerted on him by the snow to stop him; and (c) the work done on him by air resistance as he fell. Model him as a particle.

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$$-2.3 \times 10^{5} \mathrm{J}$$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

University of Michigan - Ann Arbor

Simon Fraser University

University of Winnipeg

McMaster University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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so here. For the first part, we want to know the work done by the Snow Silver Party the work of gravity plus the work of the snow. We know tio equal the change and kinetic energy we can solve and say the MG plus the work of the snow is going to be equal to negative 1/2 and the initial square to given that the final velocity is zero. So we can say that the work due to the snow is going to be equal to negative em times 1/2 times the initial squared plus G d. So we can say that the work due to the snow it's kind of the equal to negative 88 kilograms times 1/2 times of the initial squared, so 45 meters per second squared, plus 9.8 times the distance of 1.1 meters. And we find that the work done by the snow is equaling negative 9.5 times 10 to the fourth Jules. So this would be your answer for a The work done by the snow is, of course negative. Because here snow is providing friction and is allowing us to stop and work. The gravity is actually helping us move down the hill. So in this case, work the snow is actually providing friction. And so, for part B for Part B, we want to find me essentially the force of the snow. So we can say that the work of the snow is going to be equal to the force of the snow times the distance co sign of 180 degrees. So this will equal negative one. So that means that the force of the snow will be equal to negative work of the snow divided by D. And this is giving us negative brother positive 9.5 times 10 to the fourth jewels and then divided by D of 1.1 meters. So the force of the snow is found to be equal to 8.816 times 10 to the fourth Newton's. So this would be part of the answer to part be the force of the snow and then, for part, see, they want us to find the work of the air. So the work of the air we can say that the work of the air, plus the work of gravity equals the change in kinetic energy. And this will equal MGH plus the work of the air equaling 1/2 and the final squared. So now the air and the brother, the heir and the grab gravity are helping you move. So the work done by the air rather my apologies to work here again, gravity is helping you move. However, air is working against you. This will be calculating the work done by air resistance. Essentially so here the work done by air is going to be able to em times 1/2 the final squared minus G h. And then this is unequal. 88 kilograms times 1/2 times 45 meters per second. Quantity squared minus 9.8 times, 370 meters. And we find that the work done by air is going to be equal to negative 2.3 times 10 to the fifth Jules. So this would be our answer for part C. That is the end of the solution. Thank you for watching

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