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

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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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

EBK DIFFERENTIAL EQUATIONS

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