How can the kinematic equations be used to analyze motion in two dimensions ?

Separate the motion into one-dimensional components Apply the kinematic equations to each component

A two-dimensional vector can be split into .......... vectors.

A two-dimensional vector can be split into component vectors.

True or False? The magnitude of a resultant velocity is the sum of its two component magnitudes.

False. The components are perpendicular , so the magnitude is found using the Pythagorean theorem , not by adding the component magnitudes.

A projectile is an object moving freely under gravity in a two-dimensional plane.

Range is the horizontal displacement of a projectile.

Define time of flight .

Time of flight is the total time a projectile is in the air.

What are the horizontal velocity and horizontal acceleration of a projectile when air resistance is ignored?

Horizontal velocity is constant Horizontal acceleration is zero

What is the vertical velocity of a projectile at its maximum height, and when does this occur?

The vertical velocity is zero It occurs when half of the total time of flight has elapsed, for a projectile that lands at its launch height

The vertical and horizontal components of projectile motion are .......... of one another.

The vertical and horizontal components of projectile motion are independent of one another.

True or False? A projectile launched at an angle is momentarily at rest at its maximum height.

False. The vertical velocity is zero at maximum height, but the horizontal velocity is constant and nonzero, so the projectile is still moving.

AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 1: KinematicsVectors & Motion

Vectors & Motion (College Board AP® Physics 1: Algebra-Based): Flashcards

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FrontVectors & Motion in Two Dimensions
How can the kinematic equations be used to analyze motion in two dimensions?
BackVectors & Motion in Two Dimensions
Separate the motion into one-dimensional components
Apply the kinematic equations to each component
BackVectors & Motion in Two Dimensions
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FrontVectors & Motion in Two Dimensions
State the equation for the magnitude of a resultant velocity.
BackVectors & Motion in Two Dimensions
$v = \sqrt{v_{x}^{2} + v_{y}^{2}}$
$v$ = magnitude of the resultant velocity (m/s)
$v_{x}$ = horizontal component of velocity (m/s)
$v_{y}$ = vertical component of velocity (m/s)
FrontVectors & Motion in Two Dimensions
State the equation for the direction of a resultant velocity relative to the horizontal.
BackVectors & Motion in Two Dimensions
$θ = {tan}^{- 1} \frac{v_{y}}{v_{x}}$
$θ$ = angle from the horizontal (°)
$v_{x}$ = horizontal component of velocity (m/s)
$v_{y}$ = vertical component of velocity (m/s)

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Cards in this collection (13)

How can the kinematic equations be used to analyze motion in two dimensions?
- Separate the motion into one-dimensional components
- Apply the kinematic equations to each component
State the equation for the magnitude of a resultant velocity.
$v = \sqrt{v_{x}^{2} + v_{y}^{2}}$
- $v$ = magnitude of the resultant velocity (m/s)
- $v_{x}$ = horizontal component of velocity (m/s)
- $v_{y}$ = vertical component of velocity (m/s)
State the equation for the direction of a resultant velocity relative to the horizontal.
$θ = {tan}^{- 1} \frac{v_{y}}{v_{x}}$
- $θ$ = angle from the horizontal (°)
- $v_{x}$ = horizontal component of velocity (m/s)
- $v_{y}$ = vertical component of velocity (m/s)
A two-dimensional vector can be split into .......... vectors.
A two-dimensional vector can be split into component vectors.
True or False?
The magnitude of a resultant velocity is the sum of its two component magnitudes.
False.
The components are perpendicular, so the magnitude is found using the Pythagorean theorem, not by adding the component magnitudes.
Define projectile.
A projectile is an object moving freely under gravity in a two-dimensional plane.
Define range.
Range is the horizontal displacement of a projectile.
Define time of flight.
Time of flight is the total time a projectile is in the air.
What are the horizontal velocity and horizontal acceleration of a projectile when air resistance is ignored?
- Horizontal velocity is constant
- Horizontal acceleration is zero
What is the vertical acceleration of a projectile, and why?
It is constant at $g = 10$ m/s² downward, because the only force acting is its weight.
What is the vertical velocity of a projectile at its maximum height, and when does this occur?
- The vertical velocity is zero
- It occurs when half of the total time of flight has elapsed, for a projectile that lands at its launch height
The vertical and horizontal components of projectile motion are .......... of one another.
The vertical and horizontal components of projectile motion are independent of one another.
True or False?
A projectile launched at an angle is momentarily at rest at its maximum height.
False.
The vertical velocity is zero at maximum height, but the horizontal velocity is constant and nonzero, so the projectile is still moving.

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