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A standing vertical jump. Basketball player Darrell Griffith is on record as attaining a standing vertical jump of 1.2 $\mathrm{m}$ (4 ft). (This means that he moved upward by 1.2 $\mathrm{m}$ after his feet left the floor.) Griffith weighed 890 $\mathrm{N}(200 \mathrm{lb}) .$ (a) What was his speed as he left the floor? (b) If the time of the part of the jump before his feet left the floor was 0.300 s, what were the magnitude and direction of his acceleration (assuming it to be constant) while he was pushing against the floor? (c) Draw a free-body diagram of Griffith during the jump. (d) Use Newton's laws and the results of part (b) to calculate the force he applied to the ground during his jump.

See explanstion for result.

Physics 101 Mechanics

Chapter 4

Newton's Laws of Motion

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

Lectures

03:28

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.

04:16

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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A Standing Vertical Jump. …

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Basketball player Darrell …

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A standing vertical jump. …

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A basketball player jumps …

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Force During a Jump. An av…

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When jumping straight up f…

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Jumping to the Ground. A 7…

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A 105-kg basketball player…

03:31

An average person can reac…

08:01

Jumping to the ground. A 7…

all right, normally, right these out as I go. But on this one, I only had small type of some skin changes as we go. But I then rewrite everything so ever diagram of the person jumping. One thing when you have that is get there, uh, mass in kilograms. If they weigh 890 new moms and I divide 890 Newton's by gravity, which is 9.8. I get 90 0.8 kilograms, and then we need to strangers question. So what is this Speed leaving the floor while I have this handy equation here and white? Um, my final lost zero. I'm trying to find the initial velocity. I know the acceleration is be gonna be Gravity's gonna be working against me to bring me back down. And I know that the distance is 1.2 months zero or just 1.2 so I can go ahead and plug and chug these a bit numbers to do and I divide up the negative to tens 9 2019.6 Um, I'm gonna take square both sides, and I get 4.85 meters per second as my initial velocity. Now magnitude and direction of sorry shouldn't pushing off well, when you push off the ground, if we push off the ground at 0.3 seconds, that means we've been sitting on the ground for a minute, like building up, not minute. But you know, like a second we're building up exploration to jump off, and we know that we would start off with no velocity. So he no. Zero velocity. And then when we push off, we just said that when push off of 4.85 So that means our These are in this case RV final for the small window. And this is our be not for the small window. And then we can divide those by the elapsed time just 0.3 seconds, and that will get me 16.17 meters per second squared. Since it is positive, the direction is upward. All right, that's done, then a free body diagram. What we had the forces exerted on the person from the ground before they jump off. And then we'll do average forces because we're dealing with average acceleration, because that's what we found here average. And we know that weight is working against that person. So we have these things upward force and this downward force, resulting in the mass times acceleration of the object. So if I want to solve that, I know that some enforcement y is equal to the mass demonstration. The object. Um, as I said, here we have the upward force minus the downward force of gravity, such as those two. Add gravity that her side. And then here's where I had typos. We gotta fix things, Um, are mass. It's not 100 you know. That would be nice and easy. Our mass is so this means equal to our mass, which is 90.8 times acceleration of 16.17 plus the weight of the person, which is 8 90 Newtons the 90.8 time 16.17 It's 1468 point to and then we add to that 890 We get 2300 58 0.2 news, and that is the The force is applied onto the ground. Make force applied again. Yeah, because the upward force, my person, if the force from the ground in spite of the person, is 23 basically 60 Nunes if I'm not falling through the ground from this force, like for at least for a second term stationary enforce. That means there's an equal opposite force, right for liftoff. So because prior to leaving off, I haven't actually left the ground. So I'm This is your equal, and opposite force is on to each other and we're done.

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