140 Solutions Manual
Problem 2.92
An airplane flying horizontally at elevation
hD60
m and at a constant speed
v0D120 km=h
drops a
package
P
when passing over point
O
. Determine the time it takes for the package to hit the ground at
point B. In addition, determine the velocity of the package at B.
Solution
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Dynamics 2e 141
Problem 2.93
Stuntmen
A
and
B
are shooting a movie scene in which
A
needs to pass
a gun to
B
. Stuntman
B
is supposed to start falling vertically precisely
when
A
throws the gun to
B
. Treating the gun and the stuntman
B
as
particles, find the velocity of the gun as it leaves
A
’s hand so that
B
will catch it after falling 30 ft.
Solution
The gun and
B
drop at the same time from the same height, and are
142 Solutions Manual
Problem 2.94
The jaguar
A
leaps from
O
at speed
v0D6m=s
and angle
ˇD35ı
relative to the incline to try to intercept the panther
B
at
C
. Determine the distance
R
that the jaguar jumps from
O
to
C
(i.e.,
R
is the distance between the two points of the
trajectory that intersect the incline), given that the angle of the
incline is ✓D25ı.
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 143
Problem 2.95
If the projectile is released at
A
with initial speed
v0
and angle
ˇ
, derive the
projectile’s trajectory, using the coordinate system shown. Neglect air resistance.
Solution
Using the coordinate system indicated in the problem statement, we set up the following constant acceleration
144 Solutions Manual
Problem 2.96
A trebuchet releases a rock with mass
mD50 kg
at point
O
. The
initial velocity of the projectile is
Ev0D.45 O{C30 O|/m=s
. Neglecting
aerodynamic effects, determine where the rock will land and its time of
flight.
Solution
Referring to the coordinate system defined in the problem statement, we see that
yland
, the
y
coordinate of the
rock when it lands on the ground, is
h
. With this in mind, we can write the following constant acceleration
Dynamics 2e 145
Problem 2.97
A golfer chips the ball into the hole on the fly from the rough at the
edge of the green. Letting
˛D4ı
and
dD2:4
m, verify that the
golfer will place the ball within
10 mm
of the center of the hole if
the ball leaves the rough with a speed
v0D5:03 m=s
and an angle
ˇD41ı.
Solution
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permission of McGraw-Hill, is prohibited.
146 Solutions Manual
Problem 2.98
In a movie scene involving a car chase, a car goes over the top of a ramp
at Aand lands at Bbelow.
If
˛D20ı
and
ˇD23ı
, determine the distance
d
covered by the
car if the car’s speed at Ais 45 km=h. Neglect aerodynamic effects.
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 147
Problem 2.99
In a movie scene involving a car chase, a car goes over the top of a ramp
at Aand lands at Bbelow.
Determine the speed of the car at
A
if the car is to cover distance
dD150 ft for ˛D20ıand ˇD27ı. Neglect aerodynamic effects.
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.
148 Solutions Manual
Problem 2.100
The M777 lightweight
155 mm
howitzer is a piece of artillery whose
rounds are ejected from the gun with a speed of
829 m=s
. Assuming that
the gun is fired over a flat battlefield and ignoring aerodynamic effects,
determine (a) the elevation angle needed to achieve the maximum range,
(b) the maximum possible range of the gun, and (c) the time it would
take a projectile to cover the maximum range. Express the result for
the range as a percentage of the actual maximum range of this weapon,
which is 30 km for unassisted ammunition.
Photo credit: U.S. Army Photo
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 149
Problem 2.101
You want to throw a rock from point
O
to hit the vertical advertising
sign
AB
, which is
RD30 ft
away. You can throw a rock at the speed
v0D45 ft=s
. The bottom of the sign is
8ft
off the ground and the sign
is
14 ft
tall. Determine the range of angles at which the projectile can
be thrown in order to hit the target, and compare this with the angle
subtended by the target as seen from an observer at point
O
. Compare
your results with those found in Example 2.11.
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permission of McGraw-Hill, is prohibited.