Understand the rules of vector addition, subtraction, and multiplication.
Apply graphical methods of vector addition and subtraction to determine the displacement of moving objects.
Displacement can be determined graphically using a scale map, such as this one of the Hawaiian Islands. A journey from Hawai’i to Moloka’i has a number of legs, or journey segments. These segments can be added graphically with a ruler to determine the total two-dimensional displacement of the journey. (credit: US Geological Survey)
Vectors in two dimensions
A
vector is a quantity that has magnitude and direction. Displacement, velocity, acceleration, and force, for example, are all vectors. In one-dimensional, or straight-line, motion, the direction of a vector can be given simply by a plus or minus sign. In two dimensions (2-d), however, we specify the direction of a vector relative to some reference frame (i.e., coordinate system), using an arrow having length proportional to the vector’s magnitude and pointing in the direction of the vector.
[link] shows such a
graphical representation of a vector , using as an example the total displacement for the person walking in a city considered in
Kinematics in Two Dimensions: An Introduction . We shall use the notation that a boldface symbol, such as
, stands for a vector. Its magnitude is represented by the symbol in italics,
, and its direction by
.
Vectors in this text
In this text, we will represent a vector with a boldface variable. For example, we will represent the quantity force with the vector
, which has both magnitude and direction. The magnitude of the vector will be represented by a variable in italics, such as
, and the direction of the variable will be given by an angle
.
A person walks 9 blocks east and 5 blocks north. The displacement is 10.3 blocks at an angle
north of east.To describe the resultant vector for the person walking in a city considered in
[link] graphically, draw an arrow to represent the total displacement vector
. Using a protractor, draw a line at an angle
relative to the east-west axis. The length
of the arrow is proportional to the vector’s magnitude and is measured along the line with a ruler. In this example, the magnitude
of the vector is 10.3 units, and the direction
is
north of east.
Vector addition: head-to-tail method
The
head-to-tail method is a graphical way to add vectors, described in
[link] below and in the steps following. The
tail of the vector is the starting point of the vector, and the
head (or tip) of a vector is the final, pointed end of the arrow.
Head-to-Tail Method: The head-to-tail method of graphically adding vectors is illustrated for the two displacements of the person walking in a city considered in
[link] . (a) Draw a vector representing the displacement to the east. (b) Draw a vector representing the displacement to the north. The tail of this vector should originate from the head of the first, east-pointing vector. (c) Draw a line from the tail of the east-pointing vector to the head of the north-pointing vector to form the sum or
resultant vector
. The length of the arrow
is proportional to the vector’s magnitude and is measured to be 10.3 units . Its direction, described as the angle with respect to the east (or horizontal axis)
is measured with a protractor to be
.
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
