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A stone is thrown vertically upward with a speed of 12.5 $\mathrm{m} / \mathrm{s}$ from the edge of a cliff 75.0 $\mathrm{m}$ high $($ Fig. 49$) .$(a) How much later doesit reach the bottom ofthe cliff? $(b)$ What is itsspeed just before hitting?(c) What total distance didit travel?

a) The Stone Reaches the bottom after 5.39 seconds.b) The Stone Reaches the bottom at the speed of 40.3 $m / s$c) $90.9 \mathrm{m}$

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

Hera M.

November 3, 2021

A stone is thrown upward with an initial velocity of 19.6 meters per second. When will it reach the highest point?

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

University of Winnipeg

Lectures

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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.

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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so, at least for part A, it'll be a bit easier to say downwards is positive and so our initial velocity would be in the negative direction. It would be a negative initial velocity. Therefore, we can say that why final equals y initial plus V y initial t plus 1/2 of 80 squared In this case, a would be equal to G and G would equal positive 9.8 meters per second squared. Given that we're choosing downwards to be positive. So we can say that Ah, we know that why final is going to be equal to zero. So we can say that this equation with essentially become 4.9 meters per second squared, multiplied by T square. And then it would be minus 12.5 meters, that initial velocity times T and then minus 75.0 meters. And we know that this is gonna be equal to zero. This being equal to zero. We know that we can recognize that this is going to be a quadratic equation so you can use the sol function on your tea I 84 85 or 89 in order to solve for tea. And of course, we can just drop the units. So 4.9 t squared minus 12 0.5 T minus 75 T brother, this equals zero. So T is an equal negative. Two point 893839 other seconds and 5.390 seconds. Ah, we need to choose the positive answer because time can't be negative. So here, the time it takes the time Rather it takes for the P um, for the, uh, object to reach the ground would be 5.390 seconds. And for part B, we want to find the final velocity. So we can say that the final equals the initial plus 80. So this would be equal to negative 12.5 meters per second, plus 9.8 meters per second squared, multiplied by the tea that we just found. So five 0.390 seconds and we find that be final is gonna be equal to approximately 40.3 meters per second and then for part C, we want to find, uh, the total. The total distance traveled would be the total distance up plus the entire distance down um so the distance down will we know what the distance down will be? 75 more, 75 meters Maur than the distance up. So we can say that to find the distance up We can say that that the speed at the top of the past is going to be zero. So we can say that the final squared equals B initial squared plus two times g times. Why final minus y initial. Therefore, why final? I would be equal to why initial plus the final squared minus V initial squared divided by two times G. We know that the final squared at the top is gonna be equal to zero and then my initial would again be equal to zero. Therefore, we can say that why final would be equal to, uh, negative negative 12.5 meters per second quantity squared, divided by two times 9.80 meters per second squared. This is equaling negative 7.97 meters. Uh thus we can say that the distance up would be 79 79.97 meters in the distance down would be 75 plus 7.97 meters, so we can say that Delta Y total would be equal to 7.97 uh, plus 7.97 plus 75. And we find that this is equaling 90.9 meters. That would be the total distance traveled. That is the end of the solution. Thank you for watching.

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