Understand the rules of vector addition and subtraction using analytical methods.
Apply analytical methods to determine vertical and horizontal component vectors.
Apply analytical methods to determine the magnitude and direction of a resultant vector.
Analytical methods of vector addition and subtraction employ geometry and simple trigonometry rather than the ruler and protractor of graphical methods. Part of the graphical technique is retained, because vectors are still represented by arrows for easy visualization. However, analytical methods are more concise, accurate, and precise than graphical methods, which are limited by the accuracy with which a drawing can be made. Analytical methods are limited only by the accuracy and precision with which physical quantities are known.
Resolving a vector into perpendicular components
Analytical techniques and right triangles go hand-in-hand in physics because (among other things) motions along perpendicular directions are independent. We very often need to separate a vector into perpendicular components. For example, given a vector like
in
[link] , we may wish to find which two perpendicular vectors,
and
, add to produce it.
and
are defined to be the components of
along the
x - and
y -axes. The three vectors
,
, and
form a right triangle:
Note that this relationship between vector components and the resultant vector holds only for vector quantities (which include both magnitude and direction). The relationship does not apply for the magnitudes alone. For example, if
east,
north, and
north-east, then it is true that the vectors
. However, it is
not true that the sum of the magnitudes of the vectors is also equal. That is,
Thus,
If the vector
is known, then its magnitude
(its length) and its angle
(its direction) are known. To find
and
, its
x - and
y -components, we use the following relationships for a right triangle.
If the perpendicular components
and
of a vector
are known, then
can also be found analytically. To find the magnitude
and direction
of a vector from its perpendicular components
and
, we use the following relationships:
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
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Sekou
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Amisha
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Amisha
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Amisha
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Amisha
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Amisha
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Amisha
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Amisha
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Amisha
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Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.