Program Explanation Given information: The maximum height of the ball can reach on the Earth planet is 144 ft . Calculation: The position function can be expressed as, y ( t ) = v 0 t + 1 2 g t 2 + y 0 The velocity function can be expressed as, v ( t ) = − g t + v 0 The value of gravitational acceleration is g = 32 f t / s 2 and initial position y 0 = 0 as the ball thrown from the ground. Therefore, the velocity functionis represented below. v ( t ) = − 32 t + v 0 …... (1) The position function is represented below. y ( t ) = − 16 t 2 + v 0 t ....... (2) Consider t 0 as the time at which the ball is at highest point and the maximum height of the ball can reach on the Earth planet is 144 ft . Therefore, the velocity at time t 0 would be zero and the position at time t 0 would be 144. It can be written as, v ( t 0 ) = 0 , y ( t 0 ) = 144 ....... (3) Equate the equation (1) and equation (3) to obtain the value of t 0 . 0 = − 32 t + v 0 t = 1 32 v 0 Equate the equation (2) and equation (3). 144 = − 16 t 0 2 + v 0 t 0 ....... (4) Now substitute 1 32 v 0 for t 0 in equation (4) to obtain the value of v 0 . 144 = − 16 ( 1 32 v 0 ) 2 + v 0 1 32 v 0 144 = − 15 32 ⋅ 15 ( v 0 ) 2 v 0 = 96 Therefore, the initial velocity on both the planets is same therefore the initial velocity on the earth would be also 96

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

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Chapter 1.2, Problem 34P

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Program Description: The purpose of problem is to calculate the maximum height of the ball that can reach on the Gzyx planet.

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Chapter 1.2, Problem 33P

Chapter 1.2, Problem 35P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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Show that the substitution...Ch. 1.6 - Prob. 57P Ch. 1.6 - Prob. 58P Ch. 1.6 - Solve the differential equation dydx=xy1x+y+3 by...Ch. 1.6 - Prob. 60P Ch. 1.6 - Prob. 61P Ch. 1.6 - Prob. 62P Ch. 1.6 - Prob. 63P Ch. 1.6 - Prob. 64P Ch. 1.6 - Prob. 65P Ch. 1.6 - Prob. 66P Ch. 1.6 - Prob. 67P Ch. 1.6 - Prob. 68P Ch. 1.6 - Prob. 69P Ch. 1.6 - As in the text discussion, suppose that an...Ch. 1.6 - Prob. 71P Ch. 1.6 - Prob. 72P Ch. 1 - Prob. 1RP Ch. 1 - Prob. 2RP Ch. 1 - Prob. 3RP Ch. 1 - Prob. 4RP Ch. 1 - Prob. 5RP Ch. 1 - Prob. 6RP Ch. 1 - Prob. 7RP Ch. 1 - Prob. 8RP Ch. 1 - Prob. 9RP Ch. 1 - Prob. 10RP Ch. 1 - Prob. 11RP Ch. 1 - Prob. 12RP Ch. 1 - Prob. 13RP Ch. 1 - Prob. 14RP Ch. 1 - Prob. 15RP Ch. 1 - Prob. 16RP Ch. 1 - Prob. 17RP Ch. 1 - Prob. 18RP Ch. 1 - Prob. 19RP Ch. 1 - Prob. 20RP Ch. 1 - Prob. 21RP Ch. 1 - Prob. 22RP Ch. 1 - Prob. 23RP Ch. 1 - Prob. 24RP Ch. 1 - Prob. 25RP Ch. 1 - Prob. 26RP Ch. 1 - Prob. 27RP Ch. 1 - Prob. 28RP Ch. 1 - Prob. 29RP Ch. 1 - Prob. 30RP Ch. 1 - Prob. 31RP Ch. 1 - Prob. 32RP Ch. 1 - Prob. 33RP Ch. 1 - Prob. 34RP Ch. 1 - Prob. 35RP Ch. 1 - Prob. 36RP

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