Step 3.To get the magnitude
of the resultant, use the Pythagorean theorem:
Step 4.To get the direction of the resultant:
The following example illustrates this technique for adding vectors using perpendicular components.
Adding vectors using analytical methods
Add the vector
to the vector
shown in
[link] , using perpendicular components along the
x - and
y -axes. The
x - and
y -axes are along the east–west and north–south directions, respectively. Vector
represents the first leg of a walk in which a person walks
in a direction
north of east. Vector
represents the second leg, a displacement of
in a direction
north of east.
Strategy
The components of
and
along the
x - and
y -axes represent walking due east and due north to get to the same ending point. Once found, they are combined to produce the resultant.
Solution
Following the method outlined above, we first find the components of
and
along the
x - and
y -axes. Note that
,
,
, and
.
We find the
x -components by using
, which gives
and
Similarly, the
y -components are found using
:
and
The
x - and
y -components of the resultant are thus
and
Now we can find the magnitude of the resultant by using the Pythagorean theorem:
so that
Finally, we find the direction of the resultant:
Thus,
Discussion
This example illustrates the addition of vectors using perpendicular components. Vector subtraction using perpendicular components is very similar—it is just the addition of a negative vector.
Subtraction of vectors is accomplished by the addition of a negative vector. That is,
. Thus,
the method for the subtraction of vectors using perpendicular components is identical to that for addition . The components of
are the negatives of the components of
. The
x - and
y -components of the resultant
are thus
and
and the rest of the method outlined above is identical to that for addition. (See
[link] .)
Analyzing vectors using perpendicular components is very useful in many areas of physics, because perpendicular quantities are often independent of one another. The next module,
Projectile Motion , is one of many in which using perpendicular components helps make the picture clear and simplifies the physics.
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature