A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the surface at time T1 , and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified.How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer.How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer for Tstop as a single formula that contains only two independent variables, namely p and the time T1 . A ball is held at rest at some height above a horizontal surface. Once the ball is released, it falls under gravity, hits the surface at time \( T_1 \), and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction \( p \) (with \( 1>p>0 \)) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc.) that are left unspecified.1. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer.2. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time \( T_{\text{stop}} \)? Give your answer for \( T_{\text{stop}} \) as a single formula that contains only two independent variables, namely \( p \) and the time \( T_1 \).

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Description: A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the surface at time T1 , and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fracti

Given that: Time taken for first fall=T1Fraction of energy lost per each collision=p (0<p<1)

Answered: A ball is held at rest at some height…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the surface at time T₁, and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified.

How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer.
How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time T_stop? Give your answer for T_stopas a single formula that contains only two independent variables, namely p and the time T₁.

A ball is held at rest at some height above a horizontal surface. Once the ball is released, it falls under gravity, hits the surface at time \( T_1 \), and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction \( p \) (with \( 1>p>0 \)) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc.) that are left unspecified.

1. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer.

2. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time \( T_{\text{stop}} \)? Give your answer for \( T_{\text{stop}} \) as a single formula that contains only two independent variables, namely \( p \) and the time \( T_1 \).

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