A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. Assuming air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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2. The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification
of Newton's Law of Cooling is
dT
2 of 2
= kS(T – Tm),
dt
0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time.
Initially, the temperature of the coffee is 200° F. The exposed surface area of the coffee in cup B is twice the
surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 120° F. If Tm = 70°
F, then what is the temperature of the coffee in cup B after 30 min?
(Turn Over)
3. A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. ASsuming
air resistance is proportional to velocity, with k =
1/128, find the maximum height attained by the stone.
4. The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming
that the carrying capacity for the world population is 50 billion, the logistic differential equation
dP
= kP(50 – P)
dt
models the population of the world P(t) (measured in billions), where t is the number of years after 1990. Solve
this differential equation for P(t) and use this solution to predict what the population will be in 2050 according
to this model.
Transcribed Image Text:3:51 Search Done Written Assignment 3-1 (1... •.. 2. The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of Newton's Law of Cooling is dT 2 of 2 = kS(T – Tm), dt 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 200° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 120° F. If Tm = 70° F, then what is the temperature of the coffee in cup B after 30 min? (Turn Over) 3. A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. ASsuming air resistance is proportional to velocity, with k = 1/128, find the maximum height attained by the stone. 4. The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming that the carrying capacity for the world population is 50 billion, the logistic differential equation dP = kP(50 – P) dt models the population of the world P(t) (measured in billions), where t is the number of years after 1990. Solve this differential equation for P(t) and use this solution to predict what the population will be in 2050 according to this model.
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