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A stone is dropped from the roof of a high building. A secondstone is dropped 1.50 s later. How far apart are the stoneswhen the second one has reached a speed of 12.0 $\mathrm{m} / \mathrm{s} ?$

$29.0 \mathrm{m}$

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

Nikki J.

September 12, 2020

Cornell University

University of Washington

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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03:37

So the set up here, IHS, we have, uh, one stone, so I'll just say stone one and stone too. And stone one is dropped first and then stone to has dropped 1.5 seconds later. And we want to know how far apart they are when stone to has a speed of 12 meters per second. So, first of all, I know that the acceleration for both of them was minus G. I also know their initial velocity is both zero and for stone to I know our final velocity. Well, our final speed is 12 meters per second, but we're falling down, so that means the velocity is gonna be negative 12 meters per second. And now I can figure out how far stone to has gone when it reaches that velocity by saying our final velocity squared is our initial velocity squared plus to a delta Y I'm looking for delta y here. So the f is 12 uh, zero is zero. And, uh, our acceleration is minus G. So C minus two times nine point age. I'm still toe. Why? And if we solve this would get 1 44 It's negative. Two times 9.8 times delta. Why? So delta y is negative 7.34 meters. Now, we also know from this we can get the time it takes to reach that position. So we can say Delta. Why is v zero t plus 1/2 A t squared? And we already have all the information we need here to solve for t So minus 7.34 our initial velocity is still zero. So that that term goes away. Ah, and now we have minus half times 9.8. I'm t squared and Sophie Salford T so t squared is about 1.5. So tea is 1.22 seconds. And now we can plug in this time into stone one on figure out what positions, Stone One is that however, you have to remember that it was dropped first. So if we say for stone, one are Delta Y. This is Delta y two over here. Else they don't await one, uh, same equation, and we're looking for Delta y one r B zero is zero same minus 1/2 times 9.8 and R t. Now is this time we got for stone to Plus the 1.5 2nd had start This don't had And so if we solve this now we get dealt a white one. Uh, it's gonna equal 36.25 negative. Right? Could we get negative here? Yep. That's gonna be negative. Uh, 36.25 meters. And so we know we know neither of 36.25 and egg of 7.34 So if we want to find, uh, how much they're separated by weaken, do Delta y Tu minus delta. Why? One? It's minus 7.34 minus negative. 36.25 You could also deal with positive numbers and you get the same results. Um, but I like to be consistent with signs. And so here we get 28.9 meters for the separation of the two stones. And that's when the velocity of stone to is told meters per second. This is how far they're separated by

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