Chapter 3: Motion in Two Dimensions and Vectors

Flashcards introducing key vocabulary and concepts for vectors, vector operations, vector components, projectile motion, and relative velocity.

Scalar

A physical quantity that can be completely described by a single number or magnitude, such as mass, age, or temperature.

Vector

A physical quantity that must be described by both a magnitude and a direction, such as velocity or gravitational force.

Vector Magnitude

A positive scalar quantity, represented as $v$, that indicates the numerical length or size of a vector.

Graphical Vector Addition

A method of combining vectors by placing the tail of one vector at the tip of another; the resultant vector &\mathbf{D}& extends from the tail of the first vector to the tip of the final vector.

Vector Subtraction

The process of adding the negative of a vector to another vector, expressed mathematically as &\mathbf{A} - \mathbf{B} = \mathbf{A} + (-\mathbf{B})&.

Vector Components

The perpendicular parts of a vector projected along coordinate axes ($A_x$ along the x-axis and $A_y$ along the y-axis) that geometrically sum to equal the original vector.

Analytical Vector Addition

A method of vector addition where individual vector components along each axis are summed independently ($C_x = A_x + B_x$ and $C_y = A_y + B_y$) to determine the resultant vector.

Projectile Motion

Two-dimensional motion under constant vertical acceleration ($a_y = -g$) and zero horizontal acceleration ($a_x = 0$), assuming air resistance is negligible.

Parabolic Trajectory Equation

The mathematical formula describing the trajectory of a projectile, given by $y = \left(\frac{v_{y0}}{v_x}\right)x - \left(\frac{g}{2v_x^2}\right)x^2$.

Relative Velocity

The velocity of an object measured relative to a chosen reference frame, calculated by linking relative frames through subscript addition such as $\mathbf{v}_{pg} = \mathbf{v}_{pw} + \mathbf{v}_{wg}$.