Explanation Given information: The position of the object above the ground is, M ( t ) = 100 − a 2 t 2 Where a denotes the acceleration due to gravity and t denotes the time. The acceleration due to gravity on Mars’ moon Deimosis 2.15 × 10 − 3 m/sec 2 . Formula used: Differentiation of the position of an object is the speed of the object at time t . Calculation: It is provided that the position of the object above the ground is, M ( t ) = 100 − a 2 t 2 Where a denotes the acceleration due to gravity and t denotes the time. The acceleration due to gravity on the moon is 2.15 × 10 − 3 m/sec 2 . The time when the object hits the ground is equal to when the position of object is zero that is M ( t ) = 0 . Substitute M ( t ) = 0 in the equation M ( t ) = 100 − a 2 t 2 and solve for t for the provided value of acceleration. 0 = 100 − a 2 t 2 100 = 2.15 × 10 − 3 2 t 2 t = ± 305 Since time cannot be negative so time when the object hits the ground is t = 305 s . Recall the differentiation of the position of an object is the speed of the object at time t . Differentiate M ( t ) = 100 − a 2 t 2 with respect to t , apply power rule of differentiation, d d x x n = n x n − 1

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

Publisher: Cengage Learning

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Chapter 2.4, Problem 38E

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To calculate: The time when an object hits the ground of Mars’ moon Deimos when it is dropped from a height of 100 m with acceleration 2.15×10−3m/sec2 and speed of the object at that time.

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Chapter 2.4, Problem 37E

Chapter 2.4, Problem 39E

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Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

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The time when an object hits the ground of Mars’ moon Deimos when it is dropped from a height of 100 m with acceleration 2.15 × 10 − 3 m/sec 2 and speed of the object at that time.

Solution Summary: The author calculates the time when an object hits the ground of Mars' moon Deimos when it is dropped from a height of 100 m with acceleration 2.15 and speed of the object at that time.

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To calculate: The time when an object hits the ground of Mars’ moon Deimos when it is dropped from a height of 100 m with acceleration 2.15×10−3m/sec2 and speed of the object at that time.

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Chapter 2 Solutions