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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.
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.
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.
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.
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
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.
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.
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.
0
( ) 36 mi/h 52.8 ft/s
B
v
Motion of auto A:
0
( ) 35.2 1.8
AA A
vv at t
(1)
22
00
11
( ) ( ) 0 35.2 (1.8)
22
AA A A
xx vtat t t (2)
Motion of auto B:
0
( ) 52.8 1.2
BB B
vv at t
(3)
22
00
11
( ) ( ) 75 52.8 ( 1.2)
22
BB B B
xx vtat t t (4)
(a)
1
overtakes at .ABtt
22
111
: 35.2 0.9 75 52.8 0.6
AB
xx t t t t
2
11
1.5 17.6 75 0tt
11
3.22 s and 15.0546tt
1
15.05 st
Eq. (2):
2
35.2(15.05) 0.9(15.05)
A
x
734 ft
A
x
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.
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.
