(c) If a ball is initially thrown in the upward direction so that vo > 0, show that it reaches its maximum height when Yvo t = tmax -In (₁ (1+ Y mg (d) The terminal velocity of a baseball dropped from a high tower is measured to be 33 m/s. If the mass of the baseball is 145 grams (g) and g = 9.8 m/s², what is the value of y? (e) Using the values for m, g, and y in part (d), what would be the maximum height attained for a baseball thrown upward with an initial velocity vo = 30 m/s from a height of 2 m above the ground?
(c) If a ball is initially thrown in the upward direction so that vo > 0, show that it reaches its maximum height when Yvo t = tmax -In (₁ (1+ Y mg (d) The terminal velocity of a baseball dropped from a high tower is measured to be 33 m/s. If the mass of the baseball is 145 grams (g) and g = 9.8 m/s², what is the value of y? (e) Using the values for m, g, and y in part (d), what would be the maximum height attained for a baseball thrown upward with an initial velocity vo = 30 m/s from a height of 2 m above the ground?
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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Question
Transcribed Image Text:8. Classical Mechanics. The differential equation for the velocity v of an object of mass m,
restricted to vertical motion and subject only to the forces of gravity and air resistance, is
dv
(1)
m
-mg - yv.
dt
In Eq. (i) we assume that the drag force, -yu where y> 0 is a drag coefficient, is proportional to
the velocity. Acceleration due to gravity is denoted by g. Assume that the upward direction is
positive.
Transcribed Image Text:(c) If a ball is initially thrown in the upward direction so that vo > 0, show that it reaches its
maximum height when
Yvo
t = tmax -In
(₁
(1+
Y
mg
(d) The terminal velocity of a baseball dropped from a high tower is measured to be 33 m/s. If the
mass of the baseball is 145 grams (g) and g = 9.8 m/s², what is the value of y?
(e) Using the values for m, g, and y in part (d), what would be the maximum height attained for a
baseball thrown upward with an initial velocity vo = 30 m/s from a height of 2 m above the
ground?
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