978-0073398242 Chapter 11 Solution Manual Part 21

subject Type Homework Help
subject Pages 9
subject Words 1469
subject Authors Brian Self, David Mazurek, E. Johnston, Ferdinand Beer, Phillip Cornwell

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PROBLEM 11.149
A child throws a ball from point A with an initial
velocity v0 at an angle of 3 with the horizontal.
Knowing that the ball hits a wall at point B,
determine (a) the magnitude of the initial velocity,
(b) the minimum radius of curvature of the
trajectory.
page-pf2
PROBLEM 11.150
A projectile is fired from Point A
with an initial velocity
0
.
v
(a)
Show that the radius of curvature
of the trajectory of the projectile
reaches its minimum value at the
highest Point B of the trajectory.
(b) Denoting by
the angle
formed by the trajectory and the
horizontal at a given Point C, show
that the radius of curvature of the
trajectory at C is 3
min
/cos .

page-pf3
PROBLEM 11.151*
Determine the radius of curvature of the path described by the particle of Problem 11.95 when 0.t
PROBLEM 11.95 The three-dimensional motion of a particle is defined by the position vector
r (Rt cos
nt)i ctj (Rt sin
nt)k. Determine the magnitudes of the velocity and acceleration of the
particle. (The space curve described by the particle is a conic helix.)
page-pf4
PROBLEM 11.152*
Determine the radius of curvature of the path described by the particle
of Problem 11.96 when 0,t
A
3, and 1.B
PROBLEM 11.96
The three-dimensional motion of a particle is defined by the position
vector 2
(cos)( )(sin),
1
A
tt A Btt
t

ri
j
k where r and t are
expressed in feet and seconds, respectively. Show that the curve
described by the particle lies on the hyperboloid (y/A)2 (x/A)2
(z/B)2 1. For 3A
and 1,B
determine (a) the magnitudes of the
velocity and acceleration when 0,t
(b) the smallest nonzero value
of t for which the position vector and the velocity are perpendicular to
each other.
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PROBLEM 11.152* (Continued)
2
22
222


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PROBLEM 11.153
A satellite will travel indefinitely in a circular orbit around a planet if the normal component of the
acceleration of the satellite is equal to 2
(/)
g
Rr , where g is the acceleration of gravity at the surface of the
planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Knowing
that the diameter of the sun is 1.39 Gm and that the acceleration of gravity at its surface is 2
274 m/s ,
determine the radius of the orbit of the indicated planet around the sun assuming that the orbit is circular.
Earth: mean orbit
( ) 107u Mm/h.
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PROBLEM 11.154
A satellite will travel indefinitely in a circular orbit around a planet if the normal component of the
acceleration of the satellite is equal to 2
(/),
g
Rr where g is the acceleration of gravity at the surface of the
planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Knowing
that the diameter of the sun is 1.39 Gm and that the acceleration of gravity at its surface is 2
274 m/s ,
determine the radius of the orbit of the indicated planet around the sun assuming that the orbit is circular.
Saturn: mean orbit
( ) 34.7u Mm/h.
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PROBLEM 11.155
Determine the speed of a satellite relative to the indicated planet if the satellite is to travel indefinitely in a
circular orbit 100 mi above the surface of the planet. (See information given in Problems 11.153–11.154).
Venus: 2
29.20 ft/s ,g 3761R mi.
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PROBLEM 11.156
Determine the speed of a satellite relative to the indicated planet if the satellite is to travel indefinitely in a
circular orbit 100 mi above the surface of the planet. (See information given in Problems 11.153–11.154).
Mars: 2
12.17 ft/s ,g 2102R mi.
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PROBLEM 11.157
Determine the speed of a satellite relative to the indicated planet if the satellite is to travel indefinitely in a
circular orbit 100 mi above the surface of the planet. (See information given in Problems 11.153–11.154).
Jupiter: 2
75.35 ft/s ,g 44,432R mi.

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