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A person jumps from a fourth - story window 15.0 m above afirefighter's safety net. The survivor stretches the net 1.0 mbefore coming to rest, Fig. 46. (a) What was the averagedeceleration experienced by the survivor when she wasslowed to rest by the net? (b) What would you do tomake it safer (that is, to generate a smallerdeceleration): would you stiffen or loosenthe net? Explain.

a) $-150 \mathrm{m} / \mathrm{s}^{2}$b)"loosened"

Physics 101 Mechanics

Chapter 2

Describing Motion: Kinematics in One Dimension

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

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Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

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In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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So now we have someone who's jumping from a building, and if you jump out of the window down here, she's hitting a net which will stretch down. And this height she's jumping from its 15 meters and the net stretches one meter. And ah, we want to know her the acceleration when she hits the net. And so to do this, I first want to know velocity when she hits the net and then let me sow for the acceleration. So first of all we know are vertical displacement when she jumps is gonna be negative 15 meters because she's going down. And I'm going to say this direction is the positive. Why we also know our initial velocity zero? Because she's just standing and then jumping, right? Uh, final velocity we want to know. And we also know acceleration on Earth minus G. And we want to use an equation that will solve her velocity for final velocity. So we use this one. BF squared is the initial squared plus two a don't know why, and so are B f squared. We can just plug in. We have everything we need. This is gonna be zero squared, plus two times minus nine point h on since minus 15. So BF squared is to 94 and square root of that We get 17 0.14 meters per second about But we know that once she hits tonight, she's gonna be moving down. So this should be negative. And we can either pick a positive or negative answer here because either one squared is gonna get us to 94. And now, for the second part of this to get the acceleration, I'm gonna redefine our our knowns. So our delta Why now it's going to be negative. One meter, right? Pulling Ah, with the net stretching, Uh, this final velocity we had in the first part is now going to be our initial velocity for this and our fun of velocity. Well, she's coming to rest at the bottom of the net. That's gonna be zero, and we're looking for acceleration, and we use the same equation here. But now, instead of solving for ah, final velocity, we're solving for acceleration. So our final velocity now is zero this time, initial velocity. So it really didn't matter if we chose positive or negative, but I just want to be consistent with signs right and acceleration. We're looking for Delta Y is minus one. So we end up getting, ah, see or a it's gonna be at 1 46 That's right. 1 46.89 meters per second squared. And now I get a positive answer because I defined this direction is positive. And so that means that the net is slowing her down, which means the acceleration is in the positive direction. Where is gravity is pulling the other way? But if you if you define the direction the other way like she was when she had here, she was traveling this way you get a negative for the exhilaration. They're both the same. It just depends on which direction you define is positive. And now the second part is wondering whether you want to stiffen the net or loosen it to make it safer. And you can see this is a really big acceleration, so that's not very safe. So we want to loosen the net so that you have more time to fall, and that will lower your acceleration and the acceleration. If you get it low enough, it'll be safe. So you want the net to stretch as much as possible, and this also has. It relates to impulse and momentum if you know about that. But if not, that's OK. Ah, but that you can also explain this kind of problem with impulsive momentum as well is just acceleration. But so you want to loosen the net to make it safer, and that will, uh, loosening the net will lower the exploration, and if you tighten it, then it's like hitting the ground. That's why it's not safety at the ground. But if you have a net, then it's it's ah, you can survive.

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