(a) Explanation Given: m d v d t = m g − k v Object has velocity r 0 = 0 at time t = 0 Calculation: According to newton’s second law, m d v d t = m g − k v With, v 0 = 0 when t = 0 Solve the equation. The differential equation can be written as d v d t = g − k m v d v d t + k m v = g This is a linear differential equation in v and t For the differential equation, P ( t ) = k m v Q ( t ) = g So, the integrating factor is I ( t ) = e ∫ k n d t = e u α So, the solution is v l ( t (b) To determine To find: the distance s ( t ) the body has fallen at time t (c) To determine To find: The time it takes for the body to reach the ground from a height of 10,000ft

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 7.6, Problem 42PS

(a)

To determine

To solve: the given equation

(b)

To determine

To find: the distance s(t) the body has fallen at time t

(c)

To determine

To find: The time it takes for the body to reach the ground from a height of 10,000ft

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Chapter 7.6, Problem 41PS

Chapter 7.6, Problem 43PS

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Chapter 7 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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the given equation

Solution Summary: The author explains the solution of the differential equation, which can be written as l

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To solve: the given equation

To find: the distance s(t) the body has fallen at time t

To find: The time it takes for the body to reach the ground from a height of 10,000ft

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Chapter 7 Solutions