MasteringPhysics: Assignment Print View
Vector Addition and Subtraction
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with
them using their components. (You must first specify a coordinate system in order to find the
components of each arrow.) This problem gives you some practice with the components.
Let vectors
,
, and
. Calculate the following, and express
your answers as ordered triplets of values separated by commas.
Part A
ANSWER:
=
3.00,
-
5.00,
-
4.00
Part B
ANSWER:
=
-
5.00,4.00,0
Part C
ANSWER:
=
-
6.00,4.00,3.00
Part D
ANSWER:
=
-
3.00,
-
2.00,
-
11.0
Part E
ANSWER:
=
-
11.0,14.0,8.00
Part F
ANSWER:
=
17.0,
-
12.0,
-
6.00
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Vector Addition: Geometry and Components
Learning Goal:
To understand how vectors may be added using geometry or by representing them
with components.
Fundamentally, vectors are quantities that possess both magnitude and direction. In physics
problems, it is best to think of vectors as arrows, and usually it is best to manipulate them using
components. In this problem we consider the addition of two vectors using both of these methods.
We will emphasize that one method is easier to conceptualize and the other is more suited to
manipulations.
Consider adding the vectors
and
, which have lengths
and
, respectively, and where
makes an angle
from the direction of
.
In vector notation the sum is represented by
.
Part A
Which of the following procedures will
add the vectors
and
?
ANSWER:
Put the tail of
on
the arrow of
;
goes
from the tail of
to the
arrow of
Put the tail of
on
the tail of
;
goes
from the arrow of
to
the arrow of
Put the tail of
on
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MasteringPhysics: Assignment Print View
the tail of
;
goes
from the arrow of
to
the arrow of
Calculate the
magnitude as the sum of
the lengths and the
direction as midway
between
and
.
It is equally valid to put the tail of
on
the arrow of
; then
goes from the
tail of
to the arrow of
.
Part B
Find
, the length of
, the sum of
and
.
Hint B.1
Hint not displayed
Part B.2
Part not displayed
Express
in terms of
,
, and angle
.
ANSWER:
=
Part C
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Find the angle
that the vector
makes with vector
.
Hint C.1
Hint not displayed
Express
in terms of
and any of the quantities given in the problem introduction (
,
, and/
or
) as well as any necessary constants. Use asin for arcsine
ANSWER:
=
Part D
To manipulate these vectors using vector components, we must first choose a coordinate system.
In this case choosing means specifying the angle of the
x
axis. The
y
axis must be perpendicular to
this and by convention is oriented
radians counterclockwise from the
x
axis.
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- Fall '07
- Whittaker
- Cartesian Coordinate System, 90 degrees, otherapplications., 63.5 degrees
-
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