978-0077687342 Chapter 11 Part 7

subject Type Homework Help
subject Pages 14
subject Words 1336
subject Authors Brian Self, E. Johnston, Ferdinand Beer, Phillip Cornwell

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page-pf1
PROBLEM 11.91
The motion of a vibrating particle is defined by the position vector
(4sin ) (cos2 ) ,tt
rij where r is expressed in inches and t in
seconds. (a) Determine the velocity and acceleration when 1s.t
(b) Show that the path of the particle is parabolic.
page-pf2
PROBLEM 11.92
The motion of a particle is defined by the equations 10 5sin
x
tt
and 10 5cos ,yt
where x and y are
expresed in feet and t is expressed in seconds. Sketch the path of the particle for the time interval 02,t

and determine (a) the magnitudes of the smallest and largest velocities reached by the particle, (b) the
corresponding times, positions, and directions of the velocities.
32
52.12 10
page-pf3
PROBLEM 11.92 (Continued)
x
v
page-pf4
PROBLEM 11.92 (Continued)
x
v
page-pf5
PROBLEM 11.93
The damped motion of a vibrating particle is defined by the
position vector
/2
11
[1 1/ ( 1)] ( cos 2 ) ,
t
x
tye t
ri
j
where
t is expressed in seconds. For
1
30 mmx
and y
1
20 mm,
determine the position, the velocity, and the acceleration of the
particle when (a)
0,t
(b)
1.5 s.t
/2 /2
3
2/2
3
21
30 20 cos 2 2 sin 2 ( sin 2 4 cos 2 )
22
(1)
60 10 (4 sin 2 7.5 cos 2 )
(1)
tt
t
dt
ette tt
t
ett
t






  




 
ij
ij
1

page-pf6
PROBLEM 11.93 (Continued)
page-pf7
Problem 11.94
A girl operates a radio-controlled model car in a vacant
parking lot. The girl’s position is at the origin of the xy
coordinate axes, and the surface of the parking lot lies in
the x-y plane. The motion of the car is defined by the
position vector
23
ˆˆ
(2 2 ) (6 )rtitj 
where r and t
are expressed in meters and seconds, respectively.
Determine (a) the distance between the car and the girl
when t = 2 s, (b) the distance the car traveled in the interval
from t = 0 to t = 2 s, (c) the speed and direction of the car’s
velocity at t = 2 s, (d) the magnitude of the car’s
acceleration at t = 2 s.
SOLUTION
page-pf8
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.)
SOLUTION
nn
page-pf9
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.
SOLUTION
2
23/2
(cos cos sin )
1
3(2 sin cos ) 3 (2 cos sin )
(1)
dt t
tttt
tt t tt t
t

 
k
ij k
page-pfa
PROBLEM 11.96 (Continued)
page-pfb
PROBLEM 11.97
An airplane used to drop water on brushfires is flying
horizontally in a straight line at 180 mi/h at an altitude of
300 ft. Determine the distance d at which the pilot should
release the water so that it will hit the fire at B.
SOLUTION
page-pfc
PROBLEM 11.98
A ski jumper starts with a horizontal take-off velocity of 25
m/s and lands on a straight landing hill inclined at o
30 .
Determine (a) the time between take-off and landing, (b) the
length d of the jump, (c) the maximum vertical distance
between the jumper and the landing hill.
SOLUTION
 
2 2 9.81
g
page-pfd
PROBLEM 11.99
A baseball pitching machine
“throws” baseballs with a
horizontal velocity v0. Knowing
that height h varies between 788
mm and 1068 mm, determine
(a) the range of values of v0, (b) the
values of
corresponding to
h 788 mm and h 1068 mm.
SOLUTION
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PROBLEM 11.99 (Continued)
12.2
41.11
page-pff
PROBLEM 11.100
While delivering newspapers, a
girl throws a newspaper with a
horizontal velocity v
0
. Determine
the range of values of v
0
if the
newspaper is to land between
Points B and C.
0
page-pf10
PROBLEM 11.101
Water flows from a drain spout with an initial velocity of
2.5 ft/s at an angle of 15° with the horizontal. Determine the
range of values of the distance d for which the water will
enter the trough BC.
SOLUTION
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PROBLEM 11.102
In slow pitch softball the
underhand pitch must reach a
maximum height of between 1.8
m and 3.7 m above the ground. A
pitch is made with an initial
velocity of magnitude 13 m/s
at an angle of with the
horizontal. Determine (a) if the
pitch meets the maximum height
requirement, (b) the height of the
ball as it reaches the batter.
0
v
33
page-pf12
PROBLEM 11.103
A volleyball player serves the
ball with an initial velocity v
0
of
magnitude 13.40 m/s at an angle
of 20° with the horizontal.
Determine (a) if the ball will
clear the top of the net, (b) how
far from the net the ball will land.
page-pf13
PROBLEM 11.104
A golfer hits a golf ball with an initial velocity of 160 ft/s at an angle of 25° with the horizontal. Knowing that
the fairway slopes downward at an average angle of 5°, determine the distance d between the golfer and Point B
where the ball first lands.
page-pf14
PROBLEM 11.105
A homeowner uses a snowblower to clear his
driveway. Knowing that the snow is discharged
at an average angle of 40° with the horizontal,
determine the initial velocity v
0
of the snow.
SOLUTION
0

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