Repeat Problem 36, but this time assume that air resistance is proportional to instantaneous velocity. It stands
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Data from problem 36
Suppose a small cannonball weighing 16 pounds is shot vertically upward, as shown in the following figure, with an initial velocity v0 = 300 ft/s. The answer to the question How high does the cannonball go? depends on whether we take air resistance into account.
Suppose air resistance is ignored. If the positive direction is upward, then a model for the state of the cannonball is given by d2s/dt2 = -g (equation (12) of Section 1.3). Since ds/dt = v(t) the last differential equation is the same as dv/dt = -g, where we take g = 32 ft/s2. Find the velocity v(t) of the cannonball at time t.
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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
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