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310 Solutions Manual
Problem 2.233
At the instant shown,
EvBD5O{m=s
. If
✓D25ı
, determine the speed of
A
relative to
B
in order for
A
to
travel only in the vertical direction while sliding over B.
Solution
Dynamics 2e 311
Problem 2.234
An interesting application of the relative motion equations is the
experimental determination of the speed at which rain falls. Say
you perform an experiment in your car in which you park your
car in the rain and measure the angle the falling rain makes on
your side window. Let this angle be
✓rest D20ı
. Next you drive
forward at
25 mph
and measure the new angle
✓motion D70ı
that
the rain makes with the vertical. Determine the speed of the falling
rain.
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.
312 Solutions Manual
Problem 2.235
A woman is sliding down an incline with a constant acceleration of
a0D2:3 m=s2
relative to the incline. At the same time the incline is
accelerating to the right at
1:2 m=s2
relative to the ground. Letting
✓D34ı
and
LD4
m and assuming that both the woman and the
incline start from rest, determine the horizontal distance traveled by
the woman with respect to the ground when she reaches the bottom
of the slide.
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 313
Problem 2.236
The pendulum bob
A
swings about
O
, which is a fixed point, while bob
B
swings
about
A
. Express the components of the acceleration of
B
relative to the Cartesian
component system shown with origin at the fixed point
O
in terms of
L1
,
L2
,
✓
,
,
and the necessary time derivatives of and ✓.
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.
314 Solutions Manual
Problem 2.237
Revisit Example 2.24 in which the movie’s hero is traveling on train car
A
with constant speed
vAD18 m=s
while the target
B
is moving at a constant
speed
vBD40 m=s
(so that
aBD0
). Recall that
4
s before an otherwise
inevitable collision between
A
and
B
, a projectile
P
traveling at a speed of
300 m=s
relative to
A
is shot toward
B
. Take advantage of the solution in
Example 2.24 and determine the time it takes the projectile
P
to reach
B
and the projectile’s distance traveled.
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 315
Problem 2.238
Consider the following variation of the problem in Example 2.24 in which a
movie hero needs to destroy a mobile robot
B
, except this time they are not
going to collide at
C
. Assume that the hero is traveling on the train car
A
with
constant speed
vAD18 m=s
, while the robot
B
travels at a constant speed
vBD50 m=s
. In addition, assume that at time
tD0
s the train car
A
and
the robot
B
are 72 and
160
m away from
C
, respectively. To prevent
B
from
reaching its intended target, at
tD0
s the hero fires a projectile
P
at
B
. If
P
can travel at a constant speed of
300 m=s
relative to the gun, determine the
orientation
✓
that must be given to the gun to hit
B
.Hint: An equation of
the type
sin ˇ˙Acos ˇDC
has the solution
ˇD⌥Csin1.C cos /
, if
jCcos j1, where Dtan1A.
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.
316 Solutions Manual
Problem 2.239
Consider the following variation of the problem in Example 2.24 in which a
movie hero needs to destroy a mobile robot
B
. As was done in that problem,
assume that the movie hero is traveling on the train car
A
with constant speed
vAD18 m=s
and that,
4
s before an otherwise inevitable collision at
C
, the hero
fires a projectile
P
traveling at
300 m=s
relative to
A
. Unlike Example 2.24,
assume here that the robot
B
travels with a constant acceleration
aBD10 m=s2
and that
vB.0/ D20 m=s
, where
tD0
is the time of firing. Determine the
orientation
✓
of the gun fired by the hero so that
B
can be destroyed before the
collision at C.
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 317
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.
318 Solutions Manual
Problem 2.240
A park ranger
R
is aiming a rifle armed with a tranquilizer dart
at a bear (the figure is not to scale). The bear is moving in the
direction shown at a constant speed
vBD25 mph
. The ranger fires
the rifle when the bear is at
C
at a distance of
150 ft
. Knowing
that
˛D10ı
,
ˇD108ı
, the dart travels with a constant speed of
425 ft=s
, and the dart and the bear are moving in a horizontal plane,
determine the orientation
✓
of the rifle so that the ranger can hit
the bear. Hint: An equation of the type
sin ˇ˙Acos ˇDC
has
the solution
ˇD⌥Csin1.C cos /
, if
jCcos j1
, where
Dtan1A.
Solution
We will use the Cartesian component system shown at the right with origin at
R
.We
will denote the dart by P. The velocity of the bear and of the dart are
Dynamics 2e 319
Problem 2.241
The object in the figure is called a gun tackle, and it used to be very
common on sailboats to help in the operation of front-loaded guns.
If the end at
A
is pulled down at a speed of
1:5 m=s
, determine the
velocity of
B
. Neglect the fact that some portions of the rope are not
vertically aligned.
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.
