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Boundless Physics
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Chapter 3

Two-Dimensional Kinematics

Book Version 3
By Boundless
Boundless Physics
Physics
by Boundless
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Section 1
Motion in Two Dimensions
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Constant Velocity

An object moving with constant velocity must have a constant speed in a constant direction.

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Constant Acceleration

Analyzing two-dimensional projectile motion is done by breaking it into two motions: along the horizontal and vertical axes.

Section 2
Vectors
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Components of a Vector

Vectors are geometric representations of magnitude and direction and can be expressed as arrows in two or three dimensions.

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Scalars vs. Vectors

Scalars are physical quantities represented by a single number, and vectors are represented by both a number and a direction.

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Adding and Subtracting Vectors Graphically

Vectors may be added or subtracted graphically by laying them end to end on a set of axes.

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Adding and Subtracting Vectors Using Components

It is often simpler to add or subtract vectors by using their components.

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Multiplying Vectors by a Scalar

Multiplying a vector by a scalar changes the magnitude of the vector but not the direction.

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Unit Vectors and Multiplication by a Scalar

Multiplying a vector by a scalar is the same as multiplying its magnitude by a number.

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Position, Displacement, Velocity, and Acceleration as Vectors

Position, displacement, velocity, and acceleration can all be shown vectors since they are defined in terms of a magnitude and a direction.

Section 3
Projectile Motion
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Basic Equations and Parabolic Path

Projectile motion is a form of motion where an object moves in parabolic path; the path that the object follows is called its trajectory.

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Solving Problems

In projectile motion, an object moves in parabolic path; the path the object follows is called its trajectory.

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Zero Launch Angle

An object launched horizontally at a height $H$ travels a range $v_0 \sqrt{\frac{2H}{g}}$ during a time of flight $T = \sqrt{\frac{2H}{g}}$ .

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General Launch Angle

The initial launch angle (0-90 degrees) of an object in projectile motion dictates the range, height, and time of flight of that object.

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Key Points: Range, Symmetry, Maximum Height

Projectile motion is a form of motion where an object moves in parabolic path. The path that the object follows is called its trajectory.

Section 4
Multiple Velocities
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Addition of Velocities

Relative velocities can be found by adding the velocity of the observed object to the velocity of the frame of reference it was measured in.

Relative Velocity

Relative velocity is the velocity of an object B measured with respect to the velocity of another object A, denoted as $v_{BA}$.

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Boundless Physics by Boundless
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Chapter 2
Kinematics
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Chapter 3
Two-Dimensional Kinematics
  • Motion in Two Dimensions
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The Laws of Motion
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