(a) Use the formula h = -16t² + vot to determine how long it will take the arrow to reach its maximum height. What is its maximum height? (b) Determine the height of the arrow at times t = 2s and t = 3s, and the average rate of change of the height of the arrow over the interval 2 ≤t≤ 3. (c) Using t₁ = 5, apply three iterations of Newton's Method to find a zero for h. To how many decimal places does the third approximation with Newton's Method agree with the true zero of h?
(a) Use the formula h = -16t² + vot to determine how long it will take the arrow to reach its maximum height. What is its maximum height? (b) Determine the height of the arrow at times t = 2s and t = 3s, and the average rate of change of the height of the arrow over the interval 2 ≤t≤ 3. (c) Using t₁ = 5, apply three iterations of Newton's Method to find a zero for h. To how many decimal places does the third approximation with Newton's Method agree with the true zero of h?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![An arrow is shot from the ground into the air at an initial speed of vo = 108 ft/s.
(a) Use the formula
h = -1
- 16t²
+ vot
to determine how long it will take the arrow to reach its maximum height. What is its
maximum height?
(b) Determine the height of the arrow at times t = 2s and t = 3s, and the average rate of
change of the height of the arrow over the interval 2 ≤ t ≤ 3.
(c) Using t₁ = 5, apply three iterations of Newton's Method to find a zero for h. To how
many decimal places does the third approximation with Newton's Method agree with the
true zero of h?
(d) Use the Intermediate Value Theorem to show that there exists a number c € [4, 6] such
that h(c) = 130.
(e) Using t₁ = 4 and t₂ = 6, apply five iterations of the Bisection Method to find the value
of c for which h(c) = 130. To how many decimal places does the fifth approximation with
the Bisection Method agree with the true value of c?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47b4d7d1-1f2c-4cc6-8cba-31b042786b76%2Faf287470-3d0d-4969-8f24-1bd26c112175%2Fanchnga_processed.jpeg&w=3840&q=75)
Transcribed Image Text:An arrow is shot from the ground into the air at an initial speed of vo = 108 ft/s.
(a) Use the formula
h = -1
- 16t²
+ vot
to determine how long it will take the arrow to reach its maximum height. What is its
maximum height?
(b) Determine the height of the arrow at times t = 2s and t = 3s, and the average rate of
change of the height of the arrow over the interval 2 ≤ t ≤ 3.
(c) Using t₁ = 5, apply three iterations of Newton's Method to find a zero for h. To how
many decimal places does the third approximation with Newton's Method agree with the
true zero of h?
(d) Use the Intermediate Value Theorem to show that there exists a number c € [4, 6] such
that h(c) = 130.
(e) Using t₁ = 4 and t₂ = 6, apply five iterations of the Bisection Method to find the value
of c for which h(c) = 130. To how many decimal places does the fifth approximation with
the Bisection Method agree with the true value of c?
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