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
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
