FIRST COURSE IN DIFF.EQ.-WEBASSIGN
11th Edition
ISBN: 9781337652476
Author: ZILL
Publisher: CENGAGE L
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Textbook Question
Chapter 3.1, Problem 36E
How High?—No Air Resistance Suppose a small cannonball weighing 16 pounds is shot vertically upward, as shown in Figure 3.1.13, 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.
- (a) 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.
- (b) Use the result obtained in part (a) to determine the height s(t) of the cannonball measured from ground level. Find the maximum height attained by the cannonball.
FIGURE 3.1.13 Find the maximum height of the cannonball in Problem 36
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Let v₁ = (2,-3,7,8), v2 = (3, 10, -6, 14), v3 = (0, 19, -2, 16), and v₁ = (9, -2, 1, 10).
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1-1 1
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Chapter 3 Solutions
FIRST COURSE IN DIFF.EQ.-WEBASSIGN
Ch. 3.1 - The population of a community is known to increase...Ch. 3.1 - Suppose it is known that the population of the...Ch. 3.1 - The population of a town grows at a rate...Ch. 3.1 - The population of bacteria in a culture grows at a...Ch. 3.1 - The radioactive isotope of lead, Pb-209, decays at...Ch. 3.1 - Initially 100 milligrams of a radioactive...Ch. 3.1 - Determine the half-life of the radioactive...Ch. 3.1 - Consider the initial-value problem dA/dt = kA,...Ch. 3.1 - When a vertical beam of light passes through a...Ch. 3.1 - When interest is compounded continuously, the...
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