390 Solutions Manual
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 391
Problem 2.298
A car is traveling at a constant speed
v0D210 km=h
along a circular turn
with radius
RD137
m (the figure is not to scale). The camera at
O
is
tracking the motion of the car. Letting
LD15
m, determine the camera’s
rotation rate, as well as the corresponding time rate of change of the rotation
rate when D30ı.
Solution
The orientation of the camera is described by the angle
✓
shown in the
figure at the right. Let
r
represent the distance from
O
to the car. From the
392 Solutions Manual
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 393
Problem 2.299
A plane is initially flying north with a speed
v0D430 mph
relative to the ground
while the wind has a constant speed
vWD12 mph
in the north-south direction.
The plane performs a circular turn with radius of
⇢D0:45 mi
. Assume that the
airspeed indicator on the plane measures the absolute value of the component
of the relative velocity of the plane with respect to the air in the direction of
motion. Then determine the value of the tangential component of the airplane’s
acceleration when the airplane is halfway through the turn, assuming that the
airplane maintains constant the reading of the airspeed indicator.
3
3
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.
394 Solutions Manual
Problem 2.300
A fountain has a spout that can rotate about
O
and whose angle
ˇ
is controlled so as to vary with time
according to
ˇDˇ0Œ1 Csin2.!t/ç
, with
ˇ0D15ı
and
!D0:4⇡rad=s
. The length of the spout is
LD1:5 ft
, the water flow through the spout is constant, and the water is ejected at a speed
v0D6ft=s
,
measured relative to the spout.
Determine the largest speed with which the water particles are released from the spout.
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 395
Problem 2.301
A fountain has a spout that can rotate about
O
and whose angle
ˇ
is controlled so as to vary with time
according to
ˇDˇ0Œ1 Csin2.!t/ç
, with
ˇ0D15ı
and
!D0:4⇡rad=s
. The length of the spout is
LD1:5 ft
, the water flow through the spout is constant, and the water is ejected at a speed
v0D6ft=s
,
measured relative to the spout.
Determine the magnitude of the acceleration immediately before release when ˇD15ı.
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.
Problem 2.302
A fountain has a spout that can rotate about
O
and whose angle
ˇ
is controlled so as to vary with time
according to
ˇDˇ0Œ1 Csin2.!t/ç
, with
ˇ0D15ı
and
!D0:4⇡rad=s
. The length of the spout is
LD1:5 ft
, the water flow through the spout is constant, and the water is ejected at a speed
v0D6ft=s
,
measured relative to the spout.
Determine the highest position reached by the resulting water arc.
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.
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.
398 Solutions Manual
Problem 2.303
The piston head at
C
is constrained to move along the
y
axis. Let the crank
AB
be rotating counterclockwise at a constant angular speed
P
✓D2000 rpm
,
RD3:5 in:
, and
LD5:3 in:
Obtain the angular velocity of the connecting rod
BC
by differentiating the relative position vector of
C
with respect to
B
when
✓D35ı
.
Hint: You will also need to determine the velocity of
B
and enforce the constraint
that demands that Cmove only along the yaxis.
Solution
Referring to the figure at the right, we can describe the position of
C
relative to
B
Dynamics 2e 399
Problem 2.304
A child
A
is swinging from a swing that is attached to a trolley that is free to
move along a fixed rail. Letting
LD3
m, if at a given instant
aBD47:98 m=s2
,
✓D23ı
,
P
✓D3:512 rad=s
, and
R
✓D16 rad=s2
, determine the magnitude of
the acceleration of the child relative to the rail at that instant.
Solution
The acceleration of
A
relative to
B
is most easily described by setting up a polar
coordinate system with origin at
B
, radial coordinate
r
going from
B
to
A
, and