910 Solutions Manual
Problem 5.46
Two persons
A
and
B
weighing 140 and
180 lb
, respectively, jump
off a floating platform (in the same direction) with a velocity relative
to the platform that is completely horizontal and with magnitude
v0D6ft=s
for both
A
and
B
. The floating platform weighs
800 lb
.
Assume that A,B, and the platform are initially at rest.
Neglecting the water resistance to the horizontal motion of the
platform, and knowing that
A
jumps first, determine the speed of
the platform after both Aand Bhave jumped.
Solution
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Dynamics 2e 911
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912 Solutions Manual
Problem 5.47
A
180 lb
man
A
and a
40 lb
child
C
are at the opposite ends of a
250 lb
floating platform
P
with a length
Lfp D15 ft
. The man,
child, and platform are initially at rest at a distance
ıD1ft
from a
mooring dock. The child and the man move toward each other with
the same speed
v0
relative to the platform. If the drag force due to
the water is negligible, determine the distance
d
from the mooring
dock where the child and man will meet.
Solution
Denoting the platform by
P
, we model
A
,
B
, and
P
as a system, of particles subject
to their respective weights
mAg
,
mBg
, and
mPg
, as well as the force exerted by
Dynamics 2e 913
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permission of McGraw-Hill, is prohibited.
914 Solutions Manual
Problem 5.48
A man
A
, with a mass
mAD85 kg
, and a child
C
, with a mass
mCD18 kg
, are at the opposite ends of a floating platform
P
, with
a mass
mPD150 kg
and a length
Lfp D6
m. Assume that the man,
child, and platform are initially at rest and that the resistance due
to the water to the horizontal motion of the platform is negligible.
Suppose that the man and child start moving toward each other in
such a way that the platform does not move relative to the water.
Determine the distance covered by the child to meet the man.
Solution
Dynamics 2e 915
Problem 5.49
The 28;000 lb A-10 Thunderbolt is flying at a constant speed of 375 mph when it fires a 4s burst from its
forward-facing seven-barrel Gatling gun. The gun fires
13:2 oz
projectiles at a rate of
4200 rounds=min
.
The muzzle velocity of each projectile is
3250 ft=s
. Assuming that each of the plane’s two jet engines
maintains a constant thrust of
9000 lb
, that the plane is subject to a constant air resistance while the gun
is firing (equal to that before the burst), and that the plane flies straight and level, determine the plane’s
change in velocity at the end of the 4s burst.
Solution
We denote by
mi
the combined mass of the airplane and the remaining rounds after
firing the
i
-th round. We denote by
mr
the mass of a single round. We denote by
916 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 917
Problem 5.50
A man
P
on a cart on rails is receiving packages from two men
PA
and
PB
standing on a stationary
platform. Assume that
P
and the cart have a combined weight of
350 lb
and start from rest. In addition,
suppose that
PA
throws a package
A
weighing
60 lb
, which is received by
P
with a horizontal speed
vAD4:5 ft=s
. After
P
has received the package from
PA
,
PB
throws a package
B
weighing
80 lb
, which
is received by
P
with a horizontal speed relative to
P
and in the same direction as the velocity of
P
of
5:25 ft=s
. Determine the final velocity of
P
and the cart. Neglect any friction or air resistance acting on
P
and the cart and assume that the three men are big enough that they can handle throwing around
60
and
80 lb packages.
Solution
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permission of McGraw-Hill, is prohibited.