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# Unless otherwise stated, in the following problems we ISBN: 9780321747730 43

## Solution for problem 1E Chapter 3.4

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

Step 5 of 6

##### ISBN: 9780321747730

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