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(III) A rock is dropped from a sea cliff and the sound of itstriking the ocean is heard 3.4 s later. If the speed of soundis 340 $\mathrm{m} / \mathrm{s}$ , how high is the cliff?

$y_{f}=52$ meters is the height of the sea 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

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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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(III) A rock is dropped fr…

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(II) A stone is dropped fr…

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So for the Falling rock, we're gonna say down where it says positive because it's it's much If it's falling, it's much easier to choose downwards to be positive, so downwards, positive. And then we can say that Why initial with equal zero meters? Because this is the height with from which the rock is dropped. The rock has initial velocity of zero meters per second. Ah, and we can say that the acceleration is positive is G or you can save positive 9.80 meters per second squared. And so the we can say the displacement here, why would be equal to H the heights of the cliff and the time of the fall would be equal to teeth of one. So this would equal time of fall. So we can say that H is gonna equal Why initial Plus the why initial t plus 1/2 g t squared again. This is gonna zero. There's gonna be zero that's gonna be zero. This is equaling 1/2 g t sub one squared So and then when we wanted for the sound wave, we can use the constant speed equation. We know that the velocity of sound is simply gonna be equal to Delta X Divided by Delta T Um, and this is gonna be equal to H divided by T minus teeth of one so t would be equal to the total time. And so T's of one would be equal to T uh, minus h over the velocity of sound where t equals the 3.4 seconds, uh, or 3.4 seconds is the total time elapsed dropped. Total time elapsed from dropping the rock to hearing the sound of the rock hit the ground And now we can sub weaken. Substitute this equation in No for this equation here. And at this point, we can say that H is gonna equal 1/2 g times T capital T minus h over these of s and this entire quantity is squared. And so this is going to say g over two times the velocity of sound squared Time h squared minus. I mean, let's get a new line for this. We can say g over two times velocity of sound squared H squares were That's just basically ah, foiling this out. Minus, uh g Times t divided by Visa Bess plus one times h So we're factoring on H plus 1/2 times g times the total time squared. This is equaling zero. And here were, of course, trying to solve for H. So we can say that. Um, 4.2339 times 10 to the negative H squared minus 1.98 h plus 56 0.64 equal zero. This is a quadratic equation. So we can say that So we can say that, um, the if this is a quadratic equation, we can use the quadratic formula or because this is quite complicated. We can just use the sol function on your tea I 84 85 or tea I 89 in order to solve for H weaken, simply just plug in the variables or rather, the coefficients and solved for H and H is found to be equal to 51 0.7 meters. So this would be again the height of cliff. That is the end of the solution. Thank you for watching

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