A kite flies at a constant height of 30 meters above the ground in a wind that blows it horizontally at 20 meters per second. At the instant that 50 meters of string has been let out, at what rate is the angle between the string and the ground changing?
A kite flies at a constant height of 30 meters above the ground in a wind that blows it horizontally at 20 meters per second. At the instant that 50 meters of string has been let out, at what rate is the angle between the string and the ground changing?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Question
![Decide if each of the following problems is a linearization problem, an optimization prob-
lem, a related rates problem, a graphing problem, or a Newton's method problem.
Identify. Label the problem as one of the five types or explain that it is not exactly one of
those types (and how you know).
Begin solution. For each problem, start the solution.
Linearization. State what function you would linearize and where you would linearize
it.
Optimization. Draw a diagram to define your variables. Write the function you
would optimize, including the domain of the function.
Related Rates. Draw a diagram to define your variables. Write an equation that
relates your variables.
Graphing. State the function, its domain, and any critical points in the domain.
Newton's method. State the function to which you would apply Newton's method,
your initial point, and the Newton iteration.
Other. Explain how you might use calculus to solve this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37d6a9f-32c9-4856-a6ed-e90ba5efa5a8%2F5916fcac-65c2-472f-9dc1-2027a608126d%2F6l6uzk_processed.png&w=3840&q=75)
Transcribed Image Text:Decide if each of the following problems is a linearization problem, an optimization prob-
lem, a related rates problem, a graphing problem, or a Newton's method problem.
Identify. Label the problem as one of the five types or explain that it is not exactly one of
those types (and how you know).
Begin solution. For each problem, start the solution.
Linearization. State what function you would linearize and where you would linearize
it.
Optimization. Draw a diagram to define your variables. Write the function you
would optimize, including the domain of the function.
Related Rates. Draw a diagram to define your variables. Write an equation that
relates your variables.
Graphing. State the function, its domain, and any critical points in the domain.
Newton's method. State the function to which you would apply Newton's method,
your initial point, and the Newton iteration.
Other. Explain how you might use calculus to solve this problem.
![1. A kite flies at a constant height of 30 meters above the ground in a wind that blows it
horizontally at 20 meters per second. At the instant that 50 meters of string has been
let out, at what rate is the angle between the string and the ground changing?
2. Estimate v50 using tools from calculus.
3. A pomegranate is tossed upwards at a speed of 40 ft/sec. The pomegranate starts at 4.5
feet above the ground. The height of the pomegranate is give by y(t) = –16t²+40t+4.5.
How high does the pomegranate go before it starts to fall to the ground?
4. A particle is moving along a hyperbola æy = 8. As it reaches the point (4, 2), the
y-coordinate is decreasing at a rate of 7 cm/sec. How fast is the x-coordinate of the
point changing at that instant?
5. The curve y
tan(x) crosses the line y = 2x between x =
:0 and x = T/2. Estimate
where.
6. Poi is planning to build a swimming pool. Here are some of his requirements: the
surface of the pool should be 1800 ft². Along two opposite sides, he wants the deck to
be 5 ft wide, and on the other two opposites sides, he wants the deck to be 10 ft wide.
What is the smallest piece of property on which he can place his pool?
6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37d6a9f-32c9-4856-a6ed-e90ba5efa5a8%2F5916fcac-65c2-472f-9dc1-2027a608126d%2Fu99b0c_processed.png&w=3840&q=75)
Transcribed Image Text:1. A kite flies at a constant height of 30 meters above the ground in a wind that blows it
horizontally at 20 meters per second. At the instant that 50 meters of string has been
let out, at what rate is the angle between the string and the ground changing?
2. Estimate v50 using tools from calculus.
3. A pomegranate is tossed upwards at a speed of 40 ft/sec. The pomegranate starts at 4.5
feet above the ground. The height of the pomegranate is give by y(t) = –16t²+40t+4.5.
How high does the pomegranate go before it starts to fall to the ground?
4. A particle is moving along a hyperbola æy = 8. As it reaches the point (4, 2), the
y-coordinate is decreasing at a rate of 7 cm/sec. How fast is the x-coordinate of the
point changing at that instant?
5. The curve y
tan(x) crosses the line y = 2x between x =
:0 and x = T/2. Estimate
where.
6. Poi is planning to build a swimming pool. Here are some of his requirements: the
surface of the pool should be 1800 ft². Along two opposite sides, he wants the deck to
be 5 ft wide, and on the other two opposites sides, he wants the deck to be 10 ft wide.
What is the smallest piece of property on which he can place his pool?
6.
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