An airplane pilot fell 370 m after jumping from an aircraft wi...

Question

An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 82 kg and his terminal velocity was 45 m/s, estimate:
(c) the work done on him by air resistance as he fell. Model him as a particle.

(c) the work done on him by air resistance as he fell. Model him as a particle.

Accepted Answer

Welcome back. Everyone in this problem. A 47 kg dog accidentally jumped off a helicopter at a height of 410 m. Fortunately, it landed in a haystack, burying itself 1.5 m inside and survived. Given that the terminal or its terminal velocity was 49 m per second. Calculate the work done on the dog by ir resistance during its fall for simplicity, assume that the dog was a particle for our answer choices. A says that the work done is negative 1.9 multiplied by 10 to the fifth Joules B negative 1.3 multiplied by 10 to the fifth Joules C 1.3 multiplied by 10 to the fifth Joels and D 1.9 multiplied by 10 to the fifth Joules. No, let's try to visualize what's going on here. We're thinking about a dog that jumped from a helicopter accidentally, unfortunately, and we're treating the dog as a particle. OK. So let's say that this is the dog and our dog landed in a haystack. OK? So let's say this is our haystack. So eventually our dog gets somewhere here and we know that the distance the dog jumped from was it was from a height of 410 m. Ok. And when the dog landed in the haystack, it buried itself 1.5 m inside. So that height inside the haystack, let's say that it's 1.5 m. Ok. We also know that the dog, it weighs 47 kg, ok. So the mass of the dog is 47 kg and we also know that its terminal velocity was 49 m per second. In other words, as soon as the dog was about to enter the haystack, OK. Then VT let's call VT, the terminal velocity would be equal to 49 m per second. OK. And what we are trying to find is over this period, we are trying to figure out the work that was done. Now let's ask ourselves, what do we know about work? What do we know about work and speed? Because notice here we have information about the terminal velocity. Well, recall that according to the work energy theorem, the total work done would be equal to the change in kinetic energy. OK. Now, we know we also know that kinetic energy is equal to half of MV squared. OK. So now if we think about it, if we can figure out the kinetic energy or the change in kinetic energy, we should be able to get an idea of the work that's involved because here we are looking for the work done underdog by the air resistance. So there are two types of work involved. We have the work done by air resistance and we also have the work done by gravity. OK. So if we can find a change in kinetic energy, we can equate it to the total work. And thus figure out the work done underdog by air resistance. Now let's first find our change in kinetic energy. So a change in kinetic energy then is going to be the difference between the initial kinetic energy which would be half of M multiplied by V one squared, sorry, sorry or final final kinetic energy. So half multiplied by MVT squared minus or initial kinetic energy half multiplied by MV one squared. But now remember in our problem, our dog jumped off the helicopter from that height. So here we can assume before the dog was at rest, which then means that our initial speed is zero. Thus half MV one squared is also going to be equal to zero. So with that in mind, really, our change in kinetic energy is just going to be equal to half MVT squared. No, before we work that out, we won't, we won't use it for any work here or rather we won't solve, we're gonna keep the variables until the end. Since our total work done is the change in kinetic energy. Then that means the work done by gravity. OK. And the work done by air resistance is going to be equal to half MVT squared. OK. Where W represents the work done by a resistance. In that case, that means the work done by a resistance then equals half MVT squared minus the work done by gravity. And the work done by gravity is going to be equal to the mass. Let me come back here. It's going to be equal to the mass multiplied by the acceleration due to gravity multiplied by the height. That's the definition for the work done by gravity to change in our potential energy here. So if that's the case, OK, then know that we know our mass. Uh we also know our final velocity, our terminal velocity, we know the acceleration due to gravity. And here we know that the height that the dog fell is 410 m. OK? Then we can substitute those to figure out the work done by air resistance because no, that means the word done by air resistance is going to be equal to a half of. Well, we can even rewrite it. Factor om. So that's M multiplied by a half V squared minus G which is now going to be our mass 47 kg multiplied by half of our terminal velocity 49 m per second squared. OK. Minus the acceleration due to gravity. We can take that to be 9.81 m per second squared multiplied by our height 410 m. So this is going to be the work done by a resistance. Now, let's put this into our calculator. Now, when we do that, we should get that work done by air resistance is approximately equal to negative 1.3 multiplied by 10 to the fifth jewels. Taking our answer to two significant figures. That would be the work done by air resistance. If we look back at our answer choices, that means B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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