Engineering Mechanics  Dynamics
Chapter 12
(b)
Terminal velocity means
a
= 0
0
g
1
cv
term
2
−
()
=
v
term
1
c
=
v
term
100
m
s
=
Problem 1234
As a body is projected to a high altitude above the earth’s
surface
, the variation of the acceleration
of gravity with respect to altitude
y
must be taken into account. Neglecting air resistance, this
acceleration is determined from the formula
a
=
g
−
[
R
2
/
(
R+y
)
2
], where
g
is the constant
gravitational acceleration at sea level,
R
is the radius of the earth, and the positive direction is
measured upward. If
g
= 9.81 m/s
2
and
R
= 6356 km, determine the minimum initial velocity
(escape velocity) at which a projectile should be shot vertically from the earth’s surface so that it
does not fall back to the earth.
Hint:
This requires that
v
= 0 as
y
→ ∞.
Solution:
g
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.
 Spring '08
 ChristianFeldt
 Dynamics

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