38. The velocity v(t) of a skydiver is governed by the equation dv m- = mg – kv? dt - where mis the mass of the skydiver, g is gravitational acceleration, and k is a dampening constant (i.e., accounts for air friction). a. Sketch the slope field for this equation assuming 70 kg, g = 9.8 m/s², and k = 110 kg/s. b. Using the slope field, determine the value of lim v(t) for the solution v(t) satisfying v(0) = 0. that m %3D %3D %3D Note that this limiting value is known as the terminal velocity.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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476 Chapter 6 Differential Equations
a. Sketch a slope field over the region 0 <t<5 and
0 < P< 200.
b. Sketch solutions that satisfy P(0) = 0, P(0) = 10,
and P(0) = 200.
c. Use technology to obtain a better rendition of the
slope field and solutions.
d. Comment on your solutions and compare to your
work using different methods.
38. The velocity v(t) of a skydiver is governed by the
equation
du- mg – kv-
т-
dt
where mis the mass of the skydiver, g is gravitational
acceleration, and k is a dampening constant (i.e.,
accounts for air friction).
40
a. Sketch the slope field for this equation assuming
70 kg, g = 9.8 m/s², and k = 110 kg/s.
that m
b. Using the slope field, determine the value of
lim v(t) for the solution v(t) satisfying v(0) = 0.
Note that this limiting value is known as the
terminal velocity.
39. An autocatalytic chemical reaction involves two
molecules, Aand B. Let a denote the concentra-
tion of A and assume that the concentration b of
Bremains constant throughout the experiment
Transcribed Image Text:476 Chapter 6 Differential Equations a. Sketch a slope field over the region 0 <t<5 and 0 < P< 200. b. Sketch solutions that satisfy P(0) = 0, P(0) = 10, and P(0) = 200. c. Use technology to obtain a better rendition of the slope field and solutions. d. Comment on your solutions and compare to your work using different methods. 38. The velocity v(t) of a skydiver is governed by the equation du- mg – kv- т- dt where mis the mass of the skydiver, g is gravitational acceleration, and k is a dampening constant (i.e., accounts for air friction). 40 a. Sketch the slope field for this equation assuming 70 kg, g = 9.8 m/s², and k = 110 kg/s. that m b. Using the slope field, determine the value of lim v(t) for the solution v(t) satisfying v(0) = 0. Note that this limiting value is known as the terminal velocity. 39. An autocatalytic chemical reaction involves two molecules, Aand B. Let a denote the concentra- tion of A and assume that the concentration b of Bremains constant throughout the experiment
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