Dynamics 2e 11
Problem 1.6
The magnitude of the velocity vector of the car is
jEvj D 80 ft=s
. If the vector
Ev
forms an angle
D0:09 rad
with the horizontal direction, determine the Cartesian representation of
Ev
relative to the
.O{; O|/
component
system.
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12 Solutions Manual
Problem 1.7
The velocity of the car has the following representation:
EvD.8:30 O{C0:726 O| / m=s
. Determine the
magnitude of
Ev
. In addition, knowing that the angle
describes the orientation of
Ev
, determine
and
express its value in degrees.
Solution
The vector Evis given the following form
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 13
Problem 1.8
The acceleration of the car has the following representation:
EaD .3:53 O{C0:309 O|/ m=s2
. Knowing that
Eais parallel to the incline, determine the angles and and express their value in radians.
Solution
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permission of McGraw-Hill, is prohibited.
14 Solutions Manual
Problem 1.9
A jaguar
A
leaps from
O
with a velocity
Ev0
to try and intercept a panther
B
. The unit vectors
Oup
and
Ouq
are parallel and perpendicular to the incline, respectively. The unit vectors
O{
and
O|
are horizontal and
vertical, respectively. While airborne, the jaguar is subject to a constant acceleration with magnitude
g
and
direction opposite to
O|
. Denoting the magnitude of
Ev0
by
v0
and denoting the (vector) acceleration of the
jaguar by
EaA
, provide the expression of
Ev0
in the
.O{; O|/
component system and the expression of
EaA
in the
.Oup;Ouq/component system. Treat the angles ˇand as known.
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 15
Problem 1.10
The velocity vector of the airplane is
EvDv0O{
, with
v0D420 mph
. Determine the components of the
vector Evin the Ourand Oudirections for D35ı. Express the result in feet per second.
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permission of McGraw-Hill, is prohibited.
16 Solutions Manual
Problem 1.11
The motion of the telescopic arm is such that the velocity and acceleration vectors of the gear
B
are
EvD v0O|
and
EaD a0O|
, respectively, with
v0D8ft=s
and
a0D0:5 ft=s2
. Determine the components
of Evand Eain the direction of the unit vectors Ourand Oufor D32ı.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 17
Problem 1.12
At the instant shown, the velocity and acceleration vectors of the airplane have the following expressions:
EvD.215 O{C332 O| / ft=s and EaD.190 O{C76:0 O|/ ft=s2:
Use Eq. (1.17) on p. 8 to determine the angle
, the smaller of the two angles formed by
Ev
and
Ea
. Express
the result in degrees.
Solution
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permission of McGraw-Hill, is prohibited.
18 Solutions Manual
Problem 1.13
At the instant shown, when expressed via the
.Out;Oun/
component system, the
airplane’s velocity and acceleration are
EvD135 Outm=s and EaD.7:25 OutC182 Oun/m=s2:
Determine the angle
between the velocity and acceleration vectors. In addi-
tion, treating the
.Out;Oun/
and
.O{; O|/
component systems as stationary relative
to one another, express the airplane’s velocity and acceleration in the
.O{; O|/
component system.
Solution
We begin by expressing Evand Eaas follows:
EvDvtOutand EaDatOutCanOun:(1)
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 19
Problem 1.14
The components of the position vector
Er
of point
P
relative to the
.O{1;O|1/
component system are
rx1 D2ft
and ry1 D5ft. If D30ı, determine coordinates of Prelative to the .x2; y2/coordinate system.
Solution
The coordinates of
P
in the
.x2; y2/
coordinate system coincide with the components of the vector
Er
in the
component system
.O{2;O|2/
. These components can be determined via the dot product. Specifically, we have
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20 Solutions Manual
Problem 1.15
The velocity of point Prelative to frame Ais EvP =A D.14:9 O{AC19:4 O|A/ft=s, and the acceleration of
P
relative to frame
B
is
EaP =B D.3:97 O{BC4:79 O|B/ft=s2
. Frames
A
and
B
do not move relative to one
another. Determine the expressions for the velocity of
P
in frame
B
and the acceleration of
P
in frame
A
.
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permission of McGraw-Hill, is prohibited.