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Bill can throw a ball vertically at a speed 1.5 times faster than Joe can. How many times higher will Bill's ball go than Joe's?

$2.25 \approx 2.3$

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

University of Washington

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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"Joe and Bill throw i…

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Joe and Bill throw identic…

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A ball is thrown verticall…

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T A ball is thrown upward …

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A ball is thrown upward fr…

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When a ballplayer throws a…

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A boy can throw a ball a m…

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A student standing on the …

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A juggler tosses a ball ve…

So here. Let's solve for proportion. We know that B y final squared equals B. Why initial squared plus two times a g times Delta. Why? And we know that our final velocity at our peak of at the maximum height rather would be zero. So we can say that. And if Delta y we can say it, that's why it goes h our maximum height so H would simply be equal to Negative V. Why initial squared Divided by two G which here essentially h is gonna be directly proportional to the initial velocity squared. Therefore height of bill over height of Joe with equal the initial velocity for Bill squared divided by the initial velocity of Joe Squared. Ah, we know that this is going to be equal to 1.5 squared. Therefore, the height of Bill's ball is going to be equal to 2.25 times the height of Joe's ball. So if Bill can throw a ball 1.5 times this, the initial speed of the um of Joe so Bill can throw it essentially 1.5 times faster than Joe. The maximum height reached would be increased by a factor of 2.25 This would be our final answer. That is the end of the solution. Thank you for watching.

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