Vectors Flashcards
What is a scalar quantity?
A quantity that has only magnitude.
Examples include distance, speed, mass, time, and temperature.
What are some examples of scalar quantities?
- Distance
- Speed
- Mass
- Time
- Temperature
Scalar quantities do not have direction.
What is a vector quantity?
A quantity that has both magnitude and direction.
Vector quantities can be represented by vectors.
What are examples of vector quantities?
- Displacement
- Velocity
Vector quantities include both size and direction.
Is speed a scalar or vector quantity?
Scalar quantity.
Speed has magnitude only.
Is velocity a scalar or vector quantity?
Vector quantity.
Velocity has both magnitude and direction.
What do coordinates specify?
Positions.
GPS systems use coordinates to determine locations.
What types of coordinates are commonly used?
- Cartesian (x, y)
- Polar (r, θ)
These systems are used in various engineering applications.
How are Cartesian coordinates read?
Across first, then up (or down).
They indicate the location of a point relative to a fixed reference point.
What is the modulus in polar coordinates?
The value of r, denoted by mod z or |z|.
It represents how far away from the origin a point is.
How do you find the modulus from Cartesian coordinates?
Using Pythagoras’ theorem.
The formula is r = √(x² + y²).
What is the argument (or amplitude) in polar coordinates?
The angle θ.
It is denoted by arg z or amp z.
How do you convert from Cartesian to polar coordinates?
Solve a right-angled triangle with two known sides.
Use Pythagoras’ theorem and trigonometry.
What is the polar coordinate for (2, 4)?
(4.47, 63.4°)
Calculated using Pythagoras’ theorem and the tangent function.
How do you convert from polar to Cartesian coordinates?
Solve a right-angled triangle with a known longest side and angle.
Use cosine for x and sine for y.
What is the Cartesian coordinate for (13, 22.6°)?
(12, 5)
Calculated using cosine and sine functions.
What does velocity represent in terms of vectors?
It can be represented by a vector.
The length of the arrow represents speed, and the direction represents travel direction.
What is the effect of wind on aircraft velocity?
It alters the actual velocity of the aircraft.
The combined effect of wind can be represented by adding vectors.
How do you find the resultant velocity of an aircraft affected by wind?
By adding the two vectors using Pythagoras’ theorem if they are at right angles.
This gives the magnitude of the resultant velocity.
What is the magnitude of the resultant velocity for an aircraft flying north at 60 m/s with an east wind of 20 m/s?
63.24 m/s
Calculated using c² = a² + b², where a = 60 and b = 20.
What is the direction of the resultant velocity in the aircraft example?
18.4°
Calculated using the tangent function.
What are the polar coordinates of the aircraft’s resultant velocity?
(63.24, 18.4°)
Also represented as (20, 60) in Cartesian coordinates.
