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(II) Roger sees water balloons fall past his window. Henotices that each balloon strikes the sidewalk 0.83 s afterpassing his window. Roger's room is on the third floor, 15 $\mathrm{m}$above the sidewalk. (a) How fast are the balloons travelingwhen they pass Roger's window? (b) Assuming the balloonsare being released from rest, from what floor are they beingreleased? Each floor of the dorm is 5.0 $\mathrm{m}$ high.

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a) Initial Velocity $=14 m / s$b) 5 Floors

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

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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.

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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 here we want to find the initial velocity of the balloon. So here we can say that why initial is going to be equal to 15 meters and my final would be equal to ground level. So zero meters. So here we're gonna say upward is positive and of course, of upward is positive. G is gonna equal negative 9.80 meters per second squared on. We can say that we also know that t equals 0.83 seconds. Therefore, we can say that why initial equals y final plus the Y initial t plus 1/2 of g t squared. We want to find V in V Y initial so we can save E. Why initial equals y final minus y initial minus 1/2 of a T squared. Or rather, we're gonna say to simply, uh plus 1/2 gt squared and then divided by T and so v why initial will be equal to zero meters minus 15 meters minus 1/2 times negative 9.80 meters per second squared times 0.83 seconds quantity squared and again divided by 8.83 seconds. We find that b y initial is approximately negative. 14 meters per second squared. Um, speed is never negative. So here speed would of course, be equal to positive 14 meter for a second. So I would be the initial speed of the balloon. And then for part B. We want to consider the change in velocity from being released that Roger's room. So if we were to say that weekend, of course, use equation to 12 c and we can save the final squared equals the initial squared plus two times G Delta. Why we're going to say that Delta y is equaling be final squared minus V initial squared, divided by two G And this legal, uh, we know if the final is zero negative negative 14 meters per second quantity squared, divided by two times negative, 9.80 meters per second squared. And we find that delta why is equaling 10 meters? This is going to be two floors above Roger so we can say fifth floor. That is the end of the solution. Thank you for watching

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