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Unless otherwise stated, in the following problems we

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 1E Chapter 3.4

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 1E

Problem 1E

Problem

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.

An object of mass 5 kg is released from rest 1000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground?

Step-by-Step Solution:

Step 1 </p>

In this problem, we are asked to find the equation of motion and the time taken by the object to strike the ground.

Step 2</p>

The given values are

It is given that the force due to air resistance (drag force) is proportional to the velocity of the object with proportionality constant.

Therefore .

Step 3</p>

The buoyancy force (while falling downwards) acts downwards whereas the drag force acts upwards.Therefore the total force will be .

Therefore

Step 4 of 6

Chapter 3.4, Problem 1E is Solved
Step 5 of 6

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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Unless otherwise stated, in the following problems we

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