300 Solutions Manual
Problem 2.226
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
dD3ft
and
tD0:2
s, and determine the average
speed of the player so that he catches the ball.
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Dynamics 2e 301
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302 Solutions Manual
Problem 2.227
A remote controlled boat, capable of a maximum speed of
10 ft=s
in still water, is made to cross a stream
with a width
wD35 ft
that is flowing with a speed
vWD7ft=s
. If the boat starts from point
O
and keeps
its orientation parallel to the cross-stream direction, find the location of point
A
at which the boat reaches
the other bank while moving at its maximum speed. Furthermore, determine how much time the crossing
requires.
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Dynamics 2e 303
Problem 2.228
A remote controlled boat, capable of a maximum speed of
10 ft=s
in
still water, is made to cross a stream of width
wD35 ft
that is flowing
with a speed
vWD7ft=s
. The boat is placed in the water at
O
, and it is
intended to arrive at
A
by using a homing device that makes the boat
always point toward
A
. Determine the time the boat takes to get to
A
and the path it follows. Also, consider a case in which the maximum
speed of the boat is equal to the speed of the current. In such a case,
does the boat ever make it to point
A
?Hint: To solve the problem, write
EvB=W DvB=W OuA=B
, where the unit vector
OuA=B
always points from
the boat to point Aand is therefore, a function of time.
Solution
Referring to the figure at the right, we will use the Cartesian coordinate
system shown. We denote the boat by
B
and the water by
W
. Since the
304 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 305
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306 Solutions Manual
Problem 2.229
An airplane flying horizontally with a speed
vpD110 km=h
relative to the water drops a crate onto a
carrier when vertically over the back end of the ship, which is traveling at a speed vsD26 km=h relative
to the water. If the airplane drops the crate from a height
hD20
m, at what distance from the back of the
ship will the crate first land on the deck of the ship?
Solution
Referring to the figure at the right, the crate is denoted by
C
. The motion of
C
is
analyzed using a fixed Cartesian coordinate system with origin at the point where
C
Dynamics 2e 307
Problem 2.230
An airplane flying horizontally with a speed
vp
relative to the water drops a crate onto a carrier when
vertically over the back end of the ship, which is traveling at a speed
vsD32 mph
relative to the water.
The length of the carrier’s deck is
`D1000 ft
, and the drop height is
hD50 ft
. Determine the maximum
value of vpso that the crate will first impact within the rear half of the deck.
Solution
Referring to the figure at the right, the crate is denoted by
C
. The motion of
C
is
analyzed using a fixed Cartesian coordinate system with origin at the point where
C
308 Solutions Manual
Problem 2.231
An airplane is initially flying north with a speed
v0D430 mph
relative to
the ground, while the wind has a constant speed
vWD12 mph
, forming
an angle
✓D23ı
with the north-south direction. The airplane performs a
course change of
ˇD75ı
eastward while maintaining a constant reading
of the airspeed indicator. Letting
EvP=A
be the velocity of the airplane
relative to the air and assuming that the airspeed indicator measures the
magnitude of the component of
EvP=A
in the direction of motion of the
airplane, determine the speed of the airplane relative to the ground after
the course correction.
3
3
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 309
Problem 2.232
At the instant shown, block
B
is sliding over the ground with a velocity
EvB
while block
A
is sliding over
block Band has an absolute velocity EvAD.4 O{C4O|/ft=s. Determine EvBif ✓D30ı.
Solution