1.5 Vectors and Motion in Two Dimensions

• What are three examples of vector quantities?

  Displacement, velocity, force
• Match the quantity with its type:

  Displacement ↔️ Vector

  Mass ↔️ Scalar
• What does the length of a vector arrow represent?

  Magnitude
• In the graphical method, vectors are represented as arrows
• How are vectors added graphically?

  Head-to-tail
• To subtract vectors graphically, you reverse the direction of the second vector and then add.

  True
• The analytical method is more accurate than the graphical method for adding vectors.


  True
• Match the quantity with its type:

  Velocity ↔️ Vector

  Time ↔️ Scalar
• Vectors can be resolved into components using trigonometry.
• Vectors are physical quantities that have both magnitude and direction
• Scalar quantities have both magnitude and direction.

  False
• Vectors can be represented graphically using an arrow
• Steps to resolve a vector into components using trigonometry:

  1️⃣ Identify the angle between the vector and the x-axis

  2️⃣ Calculate the x-component using cosine

  3️⃣ Calculate the y-component using sine
• Understanding vectors is crucial for analyzing motion in two dimensions, such as projectile motion.
• There are two main techniques for adding and subtracting vectors: graphical and analytical.


  True
• Which theorem is used to find the magnitude of the resultant vector in the analytical method?

  Pythagorean theorem
• What are three examples of scalar quantities?

  Mass, time, temperature
• How do you add vectors graphically?

  Head-to-tail
• The horizontal component of a vector is calculated as $A_{x} =$$A \cos(\theta)$, while the vertical component is $A_{y} =$$A \sin(\theta)$, where A is the vector's magnitude
• The analytical method is more precise than the graphical method for vector addition in two-dimensional motion problems.


  True
• Match the method with its advantage:

  Graphical ↔️ Provides visual understanding

  Analytical ↔️ More precise and quantitative
• The graphical method provides visual understanding but is less precise
• The analytical method requires trigonometric calculations.

  True
• The horizontal component of a vector A is given by A_{x} = A \cos(\theta)</latex>
• The vertical component of a vector A is given by $A_{y} =$$A \sin(\theta)$
• What are the fundamental vector quantities in physics?

  Displacement, velocity, acceleration
• Acceleration is the rate of change of an object’s velocity
• Displacement, velocity, and acceleration can be resolved into components using trigonometry.


  True
• Understanding vectors is necessary for analyzing projectile motion in AP Physics 1.

  True
• To subtract vectors graphically, you reverse the direction of the second vector and then add.


  True
• In the analytical method, vectors are resolved into their x and y components
• Which theorem is used to find the magnitude of the resultant vector in the analytical method?

  Pythagorean theorem
• The analytical method is particularly useful in two-dimensional motion problems in AP Physics 1 because it allows for a more precise and quantitative analysis
• Steps for adding vectors using the graphical method

  1️⃣ Represent vectors as arrows

  2️⃣ Place the tail of one vector at the head of another
• What is the first step in the analytical method for vector addition?

  Resolve vectors into components
• The analytical method is useful for studying projectile motion because it allows independent analysis of horizontal and vertical motions.

  True
• Match the vector quantity with its definition:

  Displacement ↔️ Change in object's position

  Velocity ↔️ Rate of change of position

  Acceleration ↔️ Rate of change of velocity
• What distinguishes a vector quantity from a scalar quantity?

  Direction
• Vectors in two dimensions can be resolved into horizontal and vertical components using trigonometry
• What are the two methods for analyzing two-dimensional motion problems?

  Graphical and analytical