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Two students are asked to find the height of a particularbuilding using a barometer. Instead of using the barometeras an altitude-measuring device, they take it to the roof of thebuilding and drop it off, timing its fall. One student reports afall time of 2.0 $\mathrm{s}$ , and the other, 2.3 $\mathrm{s}$ . What $\%$ difference doesthe 0.3 s make for the estimates of the building's height?

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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

University of Michigan - Ann Arbor

Hope College

University of Sheffield

University of Winnipeg

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.

02:34

Two students are asked to …

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02:48

02:07

01:00

The students in physics cl…

02:11

Falling Object In an exper…

03:32

An object is dropped from …

03:08

02:53

In order to estimate the h…

01:47

01:34

An object is shot straight…

02:56

Altitude of a Launched Obj…

Okay, so we have to students that are throwing a barometer off a building. Ah, and if the measuring different times, uh, for the barometer to hit the ground. So one of them says it's two seconds and the other says it's 2.3 seconds. We want to find the percentage difference of the predicted height. This time difference will make. So this is the only thing that's differing between the two for now, because we know other information like our acceleration is minus G is Ron near earth surface. And we also know that the initial velocity is zero. And that's all the information we need to find the height of the building. So if we use this equation, Delta Y is V zero t plus 1/2 A T squared. Now Delta, why is that displacement and the wife final minus y initial V zero. We know zero, and we can say minus won't have g t squared now why final is when it hits the ground. So that zero, why initial is the height that we're looking for a call that each this is gonna be minus 1/2 g t squared. So h, we get a positive number, 1/2 G and I'll just say, Ah, 1/2 of 9.8 is 4.9 t squared. And so if you plug in t one Ah, here we get 4.9 times two squared, which is 19.6 meters tall. And then if we plug in 2.3 for the time taken squared, that make it a height of 25.9 to 1 meters and then we want to find the percentage difference between these two heights. So I'm gonna take Let's see. This is I'll say h one h two to find the percentage difference I'm gonna do each to minus H one divided by each one. Ah, yeah. And what this is doing is finding the difference between the two heights and how that compares to the total height. Then I also want to multiply this by 100% to turn this into a percentage because this is just going to give me a decimal. Um, so height to is 25.9 to 1 meters. Height one is 19.6 meters and we'll divide by that same 19.6. Multiply this by 100%. Now if we do, ah, this divide out the fraction we get 0.32 to 5 times 100% and then to multiply by 100% rejection with the decimal over to places. So we get 32.25 percent is the percentage difference between the two heights.

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