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Solved: A projectile of mass m = 0.11 kg shot vertically upward with initial velocity

Numerical Analysis | 9th Edition | ISBN: 9780538733519 | Authors: Richard L. Burden, J. Douglas Faires ISBN: 9780538733519 459

Solution for problem 11 Chapter 5.3

Numerical Analysis | 9th Edition

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Numerical Analysis | 9th Edition | ISBN: 9780538733519 | Authors: Richard L. Burden, J. Douglas Faires

Numerical Analysis | 9th Edition

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Problem 11

A projectile of mass m = 0.11 kg shot vertically upward with initial velocity v(0) = 8 m/s is slowed due to the force of gravity, Fg = mg, and due to air resistance, Fr = kv|v|, where g = 9.8 m/s2 and k = 0.002 kg/m. The differential equation for the velocity v is given by mv = mg kv|v|. a. Find the velocity after 0.1, 0.2, ... , 1.0 s. b. To the nearest tenth of a second, determine when the projectile reaches its maximum height and begins falling.

Step-by-Step Solution:
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Probability (Chapter 3) Rules: 1. All outcomes must lie between 0 and 1 2. The sum of all the outcomes in a sample space must equal 1 P(Event) = X/Y X  number of outcomes in the event Y  total number of outcomes in sample space Sections 3.2 – 3.4 • Union o Outcomes are either in one event or the other (in either A OR B) o A U B o Use Additive Rule to find union: ▪ P(A U B) = P(A) + P(B) – P(A ∩ B) • Intersection o Outcomes are in 2 events (in both A AND B) o A ∩ B • Complementary Events o For event A, it’s all the events that A does not occur in o Ac o Rule: P(A) + P(A ) = 1 • Mutually Exclusive events o Events

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Chapter 5.3, Problem 11 is Solved
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Textbook: Numerical Analysis
Edition: 9
Author: Richard L. Burden, J. Douglas Faires
ISBN: 9780538733519

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Solved: A projectile of mass m = 0.11 kg shot vertically upward with initial velocity