Chapter 2 Solutions
Problem 2.1
If
Evavg
is the average velocity of a point
P
over a given time interval, is
jEvavgj
, the magnitude of the average
velocity, equal to the average speed of Pover the time interval in question?
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 31
Problem 2.2
A car is seen parked in a given parking space at 8:00 A.M. on a Monday morning and is then seen parked
in the same spot the next morning at the same time. What is the displacement of the car between the two
observations? What is the distance traveled by the car during the two observations?
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.
32 Solutions Manual
Problem 2.3
Is it possible for the vector Evshown to represent the velocity of the point P?
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 33
Problem 2.4
Is it possible for the vector Eashown to be the acceleration of the point P?
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.
34 Solutions Manual
Problem 2.5
Two points Pand Qhappen to go by the same location in space (though at different times).
(a)
What must the paths of
P
and
Q
have in common if, at the location in question,
P
and
Q
have
identical speeds?
(b)
What must the paths of
P
and
Q
have in common if, at the location in question,
P
and
Q
have
identical velocities?
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 35
Problem 2.6
The position of a car traveling between two stop signs along a straight city block is given by
rD
Œ9t .45=2/ sin.2t =5/çm
, where
t
denotes time (in seconds), and where the argument of the sine function
is measured in radians. Compute the displacement of the car between
2:1
and
3:7
s, as well as between
11:1 and 12:7 s. For each of these time intervals compute the average velocity.
STOPSTOP
Solution
We denote the quantities computed between
2:1
and
3:7
s by subscript 1, and between
11:1
and
12:7
s by
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.
36 Solutions Manual
Problem 2.7
A city bus covers a
15 km
route in
45 min
. If the initial departure and final arrival points coincide, determine
the average velocity and the average speed of the bus over the entire duration of the ride. Express the
answers in m=s.
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 37
Problem 2.8
An airplane
A
is performing a loop with constant radius
⇢
. When
✓D120ı
, the speed of the airplane is
v0D210 mph
. Modeling the airplane as a point, find the velocity of the airplane at this instant using the
component system shown. Express your answer in ft=s.
Solution
38 Solutions Manual
Problem 2.9
An airplane
A
is performing a loop with constant radius
⇢D300
m. From elementary physics, we know
that the acceleration of a point in uniform circular motion (i.e., circular motion at constant speed) is
directed toward the center of the circle and has magnitude equal to
v2=⇢
, where
v
is the speed. Assuming
that
A
can maintain its speed constant and using the component system shown, provide the expressions of
the velocity and acceleration of
A
when
✓D40ı
and
jEajD3g
, where
Ea
is the acceleration of
A
and
g
is
the acceleration due to gravity.
Solution
From the problem statement, the relation between the speed and the
magnitude of the acceleration in this problem is
Dynamics 2e 39
Problem 2.10
An airplane takes off as shown following a trajectory described by equation
yDx2
, where
D2⇥104ft1
. When
xD1200 ft
, the speed of the plane is
v0D110 mph
.
Using the component system shown, provide the expression for the velocity of the airplane when
xD1200 ft. Express your answer in ft=s.
Solution
Referring to the figure at the right, we denote by
✓
the angle formed
by the velocity with the horizontal direction. We write the velocity