Chapter 3
Vectors and
TwoDimensional Motion
Quick Quizzes
1.
(c). The largest possible magnitude of the resultant occurs when the two vectors are in the
s me direction. In this case, the magnitude of the resultant is the sum of the magnitudes of
JG
and
B
J
:
R
=
A
+
B
= 20 units. The smallest possible magnitude of the resultant occurs
when the two vectors are in opposite directions, and the magnitude is the difference of the
magnitudes of
A
and
B
:
R
= 
A
–
B
= 4 units.
a
A
G
2.
(b). The resultant has magnitude
A
+
B
when
A
is oriented in the same direction as
B
.
3.
Vector
x
component
y
component
A
–
+
B
+
–
A
+
B
–
–
4.
(b). If velocity is constant, the acceleration (rate of change in velocity) is zero. An object
may have constant speed (magnitude of velocity) but still be accelerating due to a change
in direction of the velocity. If an object is following a curved path, it is accelerating
because the velocity is changing in direction.
5.
(a). Any change in the magnitude and/or direction of the velocity is an acceleration. The
gas pedal and the brake produce accelerations by altering the magnitude of the velocity.
The steering wheel produces accelerations by altering the direction of the velocity.
6.
(c). A projectile has constant horizontal velocity. Thus, if the runner throws the ball
straight up into the air, the ball maintains the horizontal velocity it had before it was
thrown (that is, the velocity of the runner). In the runner’s frame of reference, the ball
appears to go straight upward and come straight downward. To a stationary observer, the
ball follows a parabolic trajectory, moving with the same horizontal velocity as the runner
and staying above the runner’s hand.
7.
(b). The velocity is always tangential to the path while the acceleration is always directed
vertically downward. Thus, the velocity and acceleration are perpendicular only where
the path is horizontal. This only occurs at the peak of the path.
55
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3
Answers to Even Numbered Conceptual Questions
2.
The magnitudes add when
and
A
JG
B
are in the same direction. The resultant will be zero
when the two vectors are equal in magnitude and opposite in direction.
4.
The minimum sum for two vectors occurs when the two vectors are opposite in direction.
If they are unequal, their sum cannot add to zero.
6.
The component of a vector can only be equal to or less than the vector itself. It can never
be greater than the vector.
8.
The components of a vector will be equal in magnitude if the vector lies at a 45° angle with
the two axes along which the components lie.
10.
They both start from rest in the downward direction and accelerate alike in the vertical
direction. Thus, they reach the ground with the same vertical speed. However, the ball
thrown horizontally had an initial horizontal component of velocity which is maintained
throughout the motion. Thus, the ball thrown horizontally moves with the greater speed.
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 Spring '08
 pralle
 Acceleration, Velocity, Sin, Orders of magnitude, vy, twodimensional motion

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