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PROBLEM 11.36
A group of students launches a model rocket in the vertical direction. Based on tracking
data, they determine that the altitude of the rocket was 89.6 ft at the end of the powered
portion of the flight and that the rocket landed 16 s later. Knowing that the descent
parachute failed to deploy so that the rocket fell freely to the ground after reaching its
maximum altitude and assuming that
2
32.2 ft/s ,g
determine (a) the speed
1
v
of the
rocket at the end of powered flight, (b) the maximum altitude reached by the rocket.
SOLUTION
max
PROBLEM 11.37
A small package is released from rest at A and
moves along the skate wheel conveyor ABCD.
The package has a uniform acceleration of 4.8
2
m/s as it moves down sections AB and CD,
and its velocity is constant between B and C. If
the velocity of the package at D is 7.2 m/s,
determine (a) the distance d between C and D,
(b) the time required for the package to reach D.
SOLUTION
(b) For A B and C D we have
PROBLEM 11.38
A sprinter in a 100-m race accelerates uniformly for the first 35 m and then runs with
constant velocity. If the sprinter’s time for the first 35 m is 5.4 s, determine (a) his
acceleration, (b) his final velocity, (c) his time for the race.
SOLUTION
2
PROBLEM 11.39
Automobile A starts from O and
accelerates at the constant rate of
0.75 m/s2. A short time later it is
passed by bus B which is traveling
in the opposite direction at a
constant speed of 6 m/s. Knowing
that bus B passes point O 20 s after
automobile A started from there,
determine when and where the
vehicles passed each other.
SOLUTION
B
PROBLEM 11.40
In a boat race, boat A is leading boat B by 50
m and both boats are traveling at a constant
speed of 180 km/h. At 0,t
the boats
accelerate at constant rates. Knowing that
when B passes A, t8 s and 225 km/h,
A
v
determine (a) the acceleration of A, (b) the
acceleration of B.
SOLUTION
A
(b) We have
11
B
PROBLEM 11.41
As relay runner A enters the 65-ft-long exchange zone with a
speed of 30 ft/s, he begins to slow down. He hands the baton to
runner B 2.5 s later as they leave the exchange zone with the
same velocity. Determine (a) the uniform acceleration of each
of the runners, (b) when runner B should begin to run.
SOLUTION
PROBLEM 11.42
Automobiles A and B are traveling in adjacent highway lanes
and at
0t
have the positions and speeds shown. Knowing
that automobile A has a constant acceleration of
2
1.8 ft/s
and
that B has a constant deceleration of
2
1.2 ft/s ,
determine
(a) when and where A will overtake B, (b) the speed of each
automobile at that time.
SOLUTION
22
1.8 ft/s 1.2 ft/s
AB
aa
A
A
PROBLEM 11.42 (Continued)
PROBLEM 11.43
Two automobiles A and B are approaching each other in adjacent highway lanes. At t
0,
A and B are 3200 ft
apart, their speeds are
65 mi/h
A
v
and
40 mi/h,
B
v
and they are at Points P and Q, respectively. Knowing
that A passes Point Q 40 s after B was there and that B passes Point P 42 s after A was there, determine (a) the
uniform accelerations of A and B, (b) when the vehicles pass each other, (c) the speed of B at that time.
SOLUTION
2
1
B
PROBLEM 11.44
An elevator is moving upward at a constant speed of 4 m/s. A man standing 10 m
above the top of the elevator throws a ball upward with a speed of 3 m/s. Determine
(a) when the ball will hit the elevator, (b) where the ball will hit the elevator with
respect to the location of the man.
SOLUTION
Place the origin of the position coordinate at the level of the standing man, the positive direction being up.
The ball undergoes uniformly accelerated motion.
1
(b) Location of impact.
2
PROBLEM 11.45
Two rockets are launched at a fireworks display. Rocket A is launched
with an initial velocity 0
v
100 m/s and rocket B is launched t
1
seconds
later with the same initial velocity. The two rockets are timed to explode
simultaneously at a height of 300 m as A is falling and B is rising.
Assuming a constant acceleration g 9.81 2
m/s
, determine (a) the time t
1
,
(b) the velocity of B relative to A at the time of the explosion.
SOLUTION
/
BABA
/
BA
PROBLEM 11.46
Car A is parked along the northbound lane of a highway, and car B is traveling in the southbound lane at a
constant speed of 60 mi/h. At
0,t
A starts and accelerates at a constant rate
,
A
a
while at
5s,t
B begins to
slow down with a constant deceleration of magnitude
/6.
A
a
Knowing that when the cars pass each other
294 ftx
and
,
A
B
vv
determine (a) the acceleration
,
A
a
(b) when the vehicles pass each other, (c) the
distance d between the vehicles at
0.t
AB AB
PROBLEM 11.46 (Continued)
PROBLEM 11.47
The elevator shown in the figure moves downward with a constant velocity of
4 m/s. Determine (a) the velocity of the cable C, (b) the velocity of the
counterweight W, (c) the relative velocity of the cable C with respect to the
elevator, (d) the relative velocity of the counterweight W with respect to the
elevator.
/
WE
PROBLEM 11.48
The elevator shown starts from rest and moves upward with a constant
acceleration. If the counterweight W moves through 30 ft in 5 s, determine
(a) the acceleration of the elevator and the cable C, (b) the velocity of the
elevator after 5 s.
0
EE E
5
E
Problem 11.49
An athlete pulls handle A to the left with a
constant velocity of 0.5 m/s. Determine (a)
the velocity of the weight B, (b) the
relative velocity of weight B with respect
to the handle A.
/
BA
BA
Problem 11.50
An athlete pulls handle A to the left with a constant
acceleration. Knowing that after the weight B has been
lifted 4 in. its velocity is 2 ft/s, determine (a) the
accelerations of handle A and weight B (b) the velocity and
change in position of handle A after 0.5 sec.
A
PROBLEM 11.51
Slider block B moves to the right
with a constant velocity of 300
mm/s. Determine (a) the velocity
of slider block A, (b) the velocity
of portion C of the cable, (c) the
velocity of portion D of the cable,
(d) the relative velocity of portion
C of the cable with respect to slider
block A.
D
PROBLEM 11.51 (Continued)
(d) We have /
CA C A
vvv
PROBLEM 11.52
At the instant shown, slider block
B is moving with a constant
acceleration, and its speed is 150
mm/s. Knowing that after slider
block A has moved 240 mm to the
right its velocity is 60 mm/s,
determine (a) the accelerations of
A and B, (b) the acceleration of
portion D of the cable, (c) the
velocity and change in position of
slider block B after 4 s.
