Program Explanation Proof: The initial position of the stone is at the height h that is above the surface of the earth and the initial velocity is v 0 = 0 . The position function with the acceleration due to gravity can be written as, x ( t ) = 1 2 g t 2 + v 0 t ....... (1) Here, x 0 is the initial position, a is the acceleration and v 0 is the initial velocity. The initial height is x ( t ) = h . Now substitute h for x ( t ) and 0 for v 0 in equation (1) to obtain the value of t . h = 1 2 g t 2 + ( 0 ) t 2 h g = t 2 t = 2 h g The velocity function can be written as, v ( t ) = v 0 + g t

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Question

Chapter 1.2, Problem 35P

Program Plan Intro

To show: The speed of the stone is v=2gh if the stone is dropped from rest to the ground where the initial height is h that is above surface of the earth.

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Chapter 1.2, Problem 34P

Chapter 1.2, Problem 36P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Knowledge Booster

The speed of the stone is v = 2 g h if the stone is dropped from rest to the ground where the initial height is h that is above surface of the earth.

Solution Summary: The author illustrates how the initial position of the stone is at the height h that is above the earth's surface, and the velocity function with the acceleration due to gravity can be written.

To show: The speed of the stone is v=2gh if the stone is dropped from rest to the ground where the initial height is h that is above surface of the earth.

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Chapter 1 Solutions