1.5 Vectors and Motion in Two Dimensions

• Vectors are physical quantities that have both magnitude and direction
• Match the vector component with its definition:

  x-component ↔️ The horizontal part of the vector

  y-component ↔️ The vertical part of the vector
• Vector addition involves placing vectors "tip-to-tail"


  True
• The Cartesian coordinate system uses two axes: the x-axis and the y-axis
• Match the velocity component with its definition:

  \vec{v_x} ↔️ The horizontal part of the velocity vector

  \vec{v_y} ↔️ The vertical part of the velocity vector
• The resultant velocity, $\vec{v}$, can be found using the formula: $\vec{v} =$ \sqrt{\vec{v_{x}}^{2} + \vec{v_{y}}^{2}}vector
• The x-component of a vector is its vertical part

  False
• Understanding vector components is crucial for analyzing motion in two dimensions
• Vector subtraction involves placing vectors "tail-to-tail
• In the Cartesian coordinate system, coordinates are represented as (x, y) pairs

  True
• The point where the x and y axes intersect is called the origin
• The resultant velocity in two dimensions with constant velocity is calculated as $\vec{v} =$ \sqrt{\vec{v_{x}}^{2} + \vec{v_{y}}^{2}}, which uses the principle of vector addition
• Understanding the x-component and y-component of velocity is crucial for analyzing motion in two dimensions with constant velocity.


  True
• Match the vector component with its definition:

  x-component ↔️ The horizontal part of the vector

  y-component ↔️ The vertical part of the vector
• Steps for adding two vectors graphically:

  1️⃣ Place vectors "tip-to-tail"

  2️⃣ Draw the resultant vector from the tail of the first vector to the tip of the second vector
• The Cartesian coordinate system uses two axes: the x-axis and the y-axis, which intersect at the origin
• Match the coordinate with its definition:

  x-coordinate ↔️ Horizontal position relative to the origin

  y-coordinate ↔️ Vertical position relative to the origin
• The x-component of velocity, $\vec{v_{x}}$, represents the horizontal
• In projectile motion, the horizontal velocity component remains constant
• Steps for adding two vectors tip-to-tail:

  1️⃣ Place the tail of the second vector at the tip of the first vector

  2️⃣ Draw the resultant vector from the tail of the first vector to the tip of the second vector
• A vector $\vec{A}$ can be expressed as the sum of its components using the formula: $\vec{A} =$$A_{x} \hat{i} +$$A_{y} \hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in the x and y directions.unit
• To subtract vector $\vec{B}$ from $\vec{A}$, you place the tails of both vectors together and draw the vector from the tip of \vec{B}</latex> to the tip of $\vec{A}$.


  True
• What does the x-coordinate in the Cartesian coordinate system indicate?

  Horizontal position
• Understanding the Cartesian coordinate system is crucial for analyzing motion in two dimensions.

  True
• The resultant velocity in two-dimensional motion with constant velocity can be found using vector addition.


  True
• Match the component of projectile motion with its characteristic:

  Horizontal ↔️ Constant velocity

  Vertical ↔️ Constant acceleration
• The range of a projectile is given by the formula R = \frac{\vec{v_0}^2 \sin(2\theta)}{g}</latex>.


  True
• In two-dimensional motion with constant velocity, the resultant velocity can be found using vector addition