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(I) A stone is dropped from the top of a cliff. It is seen to hithe ground below after 3.75 s. How high is the cliff?

68.9 meters height of the cliff

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

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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(II) A stone is dropped fr…

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We know that Stone has dropped from a cliff and the problem tells us that it takes 3.75 seconds to hit the ground. So I'll call that tea is 3.75 seconds. And that seems like it's all the problem gives us. However, we can figure out a few more pieces of information. We also know that the acceleration it's gonna be negative G, which is around negative 9.8 meters per second squared. We also know that, uh, when the Stone has dropped its starting with an initial velocity of zero. So it's V zero uh zero. And now for this problem, we want to know the height of the cliff. And so I'll call that Delta Y in this case because it's vertical on. That's what we're looking for. And so, with these variables in mind, I want to use this equation. That's why is going to be, ah, be zero times t plus 1/2 a T squared, and it's pretty simple. Just plug in the numbers Delta y equals zero t. So that's easy. That goes away, plus 1/2 times. I want negative 9.8 meters per second squared, Uh, and our tea is going to be 3.75 seconds. Squid. And so this gives us a value of delta y of 68.9 meters. However, it's negative and that's because it's falling down. So this delta Y is actually Ah, why final minus y initial. So I'll just call this what you call it, Why minus y zero equals negative 68.9 meters. And why initial is what we're looking for. White final, This 00 minus my initial equals negative 68.9 meters and therefore the negatives go away and we get the height of the cliff is 68.9 meters.

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