2.1 Vector Methods In One Dimension Flashcards
What is one of the fastest-growing sports in the world today?
Snowshoeing
Snowshoeing is noted for its minimal equipment requirements and ease of learning.
What are the cardiovascular benefits of snowshoeing?
You can burn up to 1000 calories per hour
This makes snowshoeing an excellent cross-training program for athletes.
What allows athletes to explore different terrains and gain a greater appreciation of the outdoors?
Snowshoeing
It also helps athletes test their limits, especially in endurance races.
In which dimension can the motions in a snowshoe race be broken up?
One-dimensional
This section focuses on studying motion in one dimension using vectors.
What do vector diagrams help visualize?
The motion of an object
Properly drawn vector diagrams enable accurate addition of vectors and determination of an object’s position.
What does a line segment with an arrowhead represent in a vector diagram?
A vector quantity
The point of origin is called the tail, and the terminal point is the tip.
What indicates the direction of a vector in a vector diagram?
The arrowhead
The length of the line segment depends on the vector’s magnitude.
Fill in the blank: The length of the line segment in a vector diagram depends on the vector’s _______.
[magnitude]
This relationship is crucial for accurately representing vector quantities.
True or False: Vector diagrams can only represent motion in two dimensions.
False
This section specifically addresses one-dimensional motion using vectors.
What are some adjectives used to describe the direction of an object’s motion?
Forward, backward, up, down, into, out of, left, right
These adjectives help in clearly defining the direction of motion.
What compass directions are commonly used in vector diagrams?
North [N], South [S], East [E], West [W]
These directions can be used to describe motion in a more standardized manner.
Which directions are usually designated as positive in this unit?
Forward, up, right, north, east
Positive directions are chosen for consistency in vector representation.
What is important to communicate when solving problems involving vectors?
The reference direction must be consistent and clearly communicated
This ensures clarity in the solution process and avoids confusion.
What are collinear vectors?
Vectors that lie along the same straight line
They may point in the same or in opposite directions.
How can vectors be added?
Graphically and algebraically
Vectors can be added as long as they represent the same quantity or measurement.
What must be true for vectors to be added together?
They must represent the same types of quantities and have the same units
This is similar to adding like terms in mathematics.
What is the sum of a series of vectors called?
Resultant vector
It is drawn from the tail of the first vector to the tip of the last vector.
Fill in the blank: A vector drawn from the tail of the first vector to the tip of the last vector is called a _______.
resultant vector
This concept is crucial in understanding how to combine multiple vectors.
What should you do before adding vectors with different units?
Convert the units of one of the vectors
This ensures that both vectors are expressed in the same units for accurate addition.
What is the process for adding vectors?
Connect them tip to tail
The plus sign in a vector equation indicates to connect the vectors in a vector diagram.
What is the total distance covered by the rugby team?
115 m
This includes all the forward and backward movements combined.
What is the displacement of the rugby team after all sprints?
35 m [forward]
Displacement considers the net change in position, not the total distance traveled.
How do you subtract collinear vectors graphically?
Two methods:
* Add the negative of one vector to the other tip to tail
* Connect the vectors tail to tail
The negative of a vector points in the opposite direction of the original vector.
In the first method of vector subtraction, what is the equation used?
Ad = d1 - d2
This equation represents the resultant vector as the difference between two vectors.
What does the negative of a vector create?
A new vector that points in the opposite direction
This is essential for graphical vector subtraction.
What is the scale conversion for measuring the resultant vector in Figure 2.9?
Convert the measured value using the scale and include the direction
This process is crucial for accurately determining the magnitude and direction of vectors.
Fill in the blank: To find the magnitude of the resultant vector, you measure with a _______.
ruler
Measuring with a ruler helps determine the length of the vector in a diagram.
What is the significance of the tip of the last vector in vector addition?
It indicates where the resultant vector ends
The tip of the last vector connects to the resultant vector, showing the overall direction and magnitude.
What is the definition of displacement?
Final position minus initial position
Displacement is calculated using the formula Ad = d - d.
In the example of sprinting drills, how far does the sprinter run initially?
40.0 m [N]
What is the total distance the sprinter covers after running, walking, and sprinting?
160.0 m [N]
How far is the sailboat initially positioned from the buoy?
15 m [right]
What distance does the sailboat sail to determine its displacement?
35 m [left]
Calculate the sailboat’s displacement algebraically.
-50 m
In terms of direction, what does a negative displacement indicate?
To the left
What is the first movement of the basketball player in the give and go?
0.75 m [right]
What is the second movement of the basketball player in the give and go?
3.50 m [left]
What distance does the bricklayer’s hand sweep back and forth?
1.70 m
How many times does the bricklayer sweep her hand back and forth?
Four times
Fill in the blank: To find displacement algebraically, use the equation Ad = d - _______.
d
When finding displacement graphically, how are the position vectors arranged?
Tail to tail
What does the resultant vector represent in the graphical method of finding displacement?
The displacement from the tip of the initial position vector to the tip of the final position vector
What scale is used in the graphical representation of displacement?
1.0 cm : 10 m
True or False: The sailboat’s displacement is 50 m to the right.
False
How do you find displacement for collinear vectors?
By subtracting initial position from final position.
What is one method to subtract vectors graphically?
By connecting them tail to tail.
What is another method to subtract vectors graphically?
By reversing the direction of the initial position vector.
In which chapter is the direction for displacement discussed?
Chapter 1.
The direction for displacement is given with respect to _______.
[initial position].
