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290 Solutions Manual
Problem 2.218
Reference frame
A
is translating relative to reference frame
B
with velocity
EvA=B
and acceleration
EaA=B
.
A particle
C
appears to be stationary relative to frame
A
. What can you say about the velocity and
acceleration of particle Crelative to frame B?
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 291
Problem 2.219
Reference frame
A
is translating relative to reference frame
B
with constant velocity
EvA=B
. A particle
C
appears to be in uniform rectilinear motion relative to frame
A
. What can you say about the motion of
particle Crelative to frame B?
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.
292 Solutions Manual
Problem 2.220
A skier is going down a slope with moguls. Let the skis be short enough for
us to assume that the skier’s feet are tracking the moguls’ profile. Then, if the
skier is skilled enough to maintain her hips on a straight-line trajectory and
vertically aligned over her feet, determine the velocity and acceleration of her
hips relative to her feet when her speed is equal to
15 km=h
. For the profile
of the moguls, use the formula
y.x/ DhI0:15x C0:125 sin.⇡x=2/ m
,
where hIis the elevation at which the skier starts the descent.
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 293
Problem 2.221
Two particles
A
and
B
are moving in a plane with arbitrary velocity vectors
EvA
and
EvB
, respectively.
Letting the rate of separation (ROS) be defined as the component of the relative velocity vector along the
line connecting particles
A
and
B
, determine a general expression for
ROS
. Express your result in terms
of
ErB=A DErBErA
, where
ErA
and
ErB
are the position vectors of
A
and
B
, respectively, relative to some
chosen fixed point in the plane of motion.
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.
294 Solutions Manual
Problem 2.222
Airplanes
A
and
B
are flying along straight lines at the same altitude and with speeds
vAD660 km=h
and
vBD550 km=h, respectively. Determine the speed of Aas perceived by Bif ✓D50ı.
3
3
3
3
Solution
3
3
3
3
Referring to the figure at the right, we use the Cartesian coordinate system
shown to express the velocities of the airplanes Aand B:
EvADvAO|and EvBDvB.sin ✓O{Ccos ✓O|/: (1)
Using relative kinematics, the velocity of Aas perceived by Bis
EvA=B DEvAEvBDvBsin ✓O{C.vAvBcos ✓/O|: (2)
The speed of
A
as perceived by
B
is the magnitude of the vector
EvA=B
. Using
the result in Eq. (2), we have
vA=B DˇˇEvA=B ˇˇDqv2
Bsin2✓C.vAvBcos ✓/2:(3)
Recalling that
vAD660 km=hD6601000
3600 m=s
,
vBD550 km=hD
5501000
3600 m=s and ✓D50ı, we can evaluate the expression in Eq. (3) to obtain
vA=B D144:7 m=s:
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 295
Problem 2.223
Three vehicles
A
,
B
, and
C
are in the positions shown and are
moving with the indicated directions. We define the rate of sepa-
ration (ROS) of two particles
P1
and
P2
as the component of the
relative velocity of, say,
P2
with respect to
P1
in the direction of
the relative position vector of
P2
with respect to
P1
, which is along
the line that connects the two particles. At the given instant, de-
termine the rates of separation
ROSAB
and
ROSCB
, that is, the
rate of separation between
A
and
B
and between
C
and
B
. Let
vAD60 mph
,
vBD55 mph
, and
vCD35 mph
. Furthermore, treat
the vehicles as particles and use the dimensions shown in the figure.
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.
296 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 297
Problem 2.224
Car
A
is moving at a constant speed
vAD75 km=h
, while car
C
is
moving at a constant speed
vCD42 km=h
on a circular exit ramp
with radius
⇢D80
m. Determine the velocity and acceleration of
C
relative to A.
Solution
Referring to the figure at the right, the
xy
frame of reference with origin
298 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 299
Problem 2.225
During practice, a player
P
punts a ball
B
with a speed
v0D25 ft=s
,
at an angle
✓D60ı
, and at a height
h
from the ground. Then the
player sprints along a straight line and catches the ball at the same height
from the ground at which the ball was initially kicked. The length
d
denotes the horizontal distance between the player’s position at the start of
the sprint and the ball’s position when the ball leaves the player’s foot.
Also, let
t
denote the time interval between the instant at which the
ball leaves the player’s foot and the instant at which the player starts
sprinting.
Assume that
dD0
and
tD0
, and determine the average speed of
the player so that he catches the ball.
Solution
