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80 Solutions Manual
Problem 2.40
The following four problems refer to a car traveling between two
stop signs, in which the car’s velocity is assumed to be given by
v.t/ DŒ9 9cos.2t=5/çm=s for 0t5⇡s.
Determine the time at which the brakes are applied and the car
starts to slow down.
STOPSTOP
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 81
Problem 2.41
The following four problems refer to a car traveling between two
stop signs, in which the car’s velocity is assumed to be given by
v.t/ DŒ9 9cos.2t=5/çm=s for 0t5⇡s.
Determine the average velocity of the car between the two stop
signs.
STOPSTOP
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
82 Solutions Manual
Problem 2.42
The following four problems refer to a car traveling between two
stop signs, in which the car’s velocity is assumed to be given by
v.t/ DŒ9 9cos.2t=5/çm=s for 0t5⇡s.
Determine
jajmax
, the maximum of the magnitude of the accel-
eration reached by the car, and determine the position(s) at which
jajmax occurs.
STOPSTOP
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 83
Problem 2.43
The acceleration of a sled is prescribed to have the following form:
aDˇpt
, where
t
is time expressed
in seconds, and
ˇ
is a constant. The sled starts from rest at
tD0
. Determine
ˇ
in such a way that the
distance traveled after 1s is 25 ft.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
84 Solutions Manual
Problem 2.44
The acceleration of a sled can be prescribed to have one of the following forms:
aDˇ1pt
,
aDˇ2t
,
and
aDˇ3t2
, where
t
is time expressed in seconds,
ˇ1D1m=s5=2
,
ˇ2D1m=s3
, and
ˇ3D1m=s4
.
The sled starts from rest at
tD0
. Determine which of the three cases allows the sled to cover the largest
distance in 1s. In addition, determine the distance covered for the case in question.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 85
Problem 2.45
A peg is constrained to move in a rectilinear guide and is given the following acceleration:
aDa0sin !t
,
where a0D20 ft=s2,!D250 rad=s, and tis time expressed in seconds.
If xD0and vD0for tD0, determine the position of the peg at tD4s.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
86 Solutions Manual
Problem 2.46
A peg is constrained to move in a rectilinear guide and is given the following acceleration:
aDa0sin !t
,
where a0D20 ft=s2,!D250 rad=s, and tis time expressed in seconds.
Determine the value of the velocity of the peg at tD0so that x.t/ is periodic.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 87
Problem 2.47
A ring is thrown straight upward from a height
hD2:5
m off the ground
and with an initial velocity
v0D3:45 m=s
. Gravity causes the ring to
have a constant downward acceleration
gD9:81 m=s2
. Determine
hmax
,
the maximum height reached by the ring.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
88 Solutions Manual
Problem 2.48
A ring is thrown straight upward from a height
hD2:5
m off the ground.
Gravity causes the ring to have a constant downward acceleration
gD
9:81 m=s2
. Letting
dD5:2
m, if the person at the window is to receive
the ring in the gentlest possible manner, determine the initial velocity
v0
the ring must be given when first released.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 89
Problem 2.49
A hot air balloon is climbing with a velocity of
7m=s
when
a sandbag (used as ballast) is released at an altitude of
305
m.
Assuming that the sandbag is subject only to gravity and that
therefore its acceleration is given by
RyDg
,
g
being the accel-
eration due to gravity, determine how long the sandbag takes to
hit the ground and its impact velocity.
Solution
Since the acceleration of the sandbag is constant and equal to
g
, position and time are related by the
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
