Resource Lesson
Freefall: Projectiles in 1-Dimension
Printer Friendly Version
A
projectile
is an object that moves through the air by virtue of its own inertia. Recall that mass is a measure of an object's inertia which is its resistance to a change in its state of motion. The term
freefall
means that the only force acting on the projectile is gravity; that is, there is no air resistance present. While in freefall, all projectiles experiences a unique value for their vertical acceleration: a = -g = -9.81 m/sec
^{2}
. The term
trajectory
means the projectile’s path through the air. If the projectile only has vertical velocity, its trajectory traces out a vertical line. When it has a constant horizontal velocity combined with a vertical velocity which is uniformly accelerated, the trajectory will be parabolic. The term
apex
means highest point in the projectile’s trajectory where its instantaneous vertical velocity equals 0.
Refer to the following information for the next four questions.
Take a moment to remember the kinematics equations for uniformly accelerated motion.
What kinematics formula relates the variables s, v
_{o}
, a and t ?
What kinematics formula relates v
_{f}
, v
_{o}
, a, and s?
What kinematics formula relates v
_{f}
, v
_{o}
, a, and t?
What kinematics formula relates s, v
_{o}
, v
_{f}
and t?
These formulas are used when the
acceleration is uniform (constant)
. Remember that acceleration is the rate of change of velocity. If the object is either losing speed while traveling in a positive direction OR gaining speed in a negative direction, a is negative.
In freefall problems, a has a value of -9.81 m/sec
^{2}
.
This value is represented by the variable
g
. Which is either called the "acceleration due to gravity" or the "gravitational field strength." Its value depends on where the projectile is located with respect to the center of the earth. The value for
g
on the surface of the earth is derived based on the formula for universal gravitation and weight.
weight = force of universal gravitation
|mg| = G(mM
_{E}
/r
^{2}
)
|g| = G(M
_{E}
/r
^{2}
)
Try it! G = 6.67 x 10
^{-11}
Nm
^{2}
/kg
^{2}
, M
_{E}
= 5.98 x 10
^{24}
kg, r = R
_{E}
= 6.37 x 10
^{6}
m
Substituting these values give us the magnitude of
g
to be approximately 9.8 m/sec
^{2}
. Since gravity pulls objects towards the center of the earth, the value of
a
used in our kinematics equations for uniformly accelerated motion when working freefall problems will be
a = - g = -9.8 m/sec
^{2}
.
Note that only the vertical motion of the projectile will experience this acceleration since gravity is a "vertical force" that attracts the projectile to the "center of the earth." For this reason, we often subscript the variable as
a
_{y}
= - 9.8 m/sec
^{2}
. Any projectile moving in two-dimensions will experience no acceleration horizontally since freefall eliminates all forces (air resistance, drag) except for the pull of gravity.
The remainder of this lesson only deals with one-dimensional, or vertical freely falling bodies, so we will just use the notation a = -9.8 m/sec
^{2}
.
For a projectile thrown vertically straight upwards, examine the sketch below which relates the graphs for the projectile's
position vs time
and its
velocity vs time
.
When doing freefall /projectile problems,
vertical velocities, v
, are
positive
when the object is traveling "up" towards the apex, and
negative
when the object is falling "down" after having reached the apex.
While the
displacement , s
, is
positive when the projectile is located "above the release height,"
negative when located "below the release height," and
equal to zero when the projectile has returned to its original release height.
Refer to the following information for the next five questions.
Identify the positions (A, B, C, D, or E) that represent each set of criteria.
v
_{f}
> 0 and s > 0
v
_{f}
< 0 and s < 0
v
_{f}
< 0 and s > 0
v
_{f}
= 0 and s > 0
v
_{f}
< 0 and s = 0
Now let's apply our knowledge to some problems that contain numerical data. In each of the following scenarios, state the values of v
_{o}
, a, and s.
A rock dropped from a 20 meter bridge falls into the river below.
A rock thrown upwards at 6 m/sec from a 20 meter bridge falls into the river below.
A rock thrown downwards at 6 m/sec from a 20 meter bridge falls into the river below.
Related Documents
Lab:
Labs -
A Photoelectric Effect Analogy
Labs -
Acceleration Down an Inclined Plane
Labs -
Ballistic Pendulum: Muzzle Velocity
Labs -
Coefficient of Friction
Labs -
Collision Pendulum: Muzzle Velocity
Labs -
Conservation of Momentum
Labs -
Cookie Sale Problem
Labs -
Flow Rates
Labs -
Freefall Mini-Lab: Reaction Times
Labs -
Freefall: Timing a Bouncing Ball
Labs -
Galileo Ramps
Labs -
Gravitational Field Strength
Labs -
Home to School
Labs -
InterState Map
Labs -
LAB: Ramps - Accelerated Motion
Labs -
LabPro: Newton's 2nd Law
Labs -
LabPro: Uniformly Accelerated Motion
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Monkey and the Hunter Animation
Labs -
Monkey and the Hunter Screen Captures
Labs -
Projectiles Released at an Angle
Labs -
Ramps: Sliding vs Rolling
Labs -
Range of a Projectile
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Rube Goldberg Challenge
Labs -
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video Lab: Ball Bouncing Across a Stage
Labs -
Video LAB: Ball Re-Bounding From a Wall
Labs -
Video Lab: Cart Push #2 and #3
Labs -
Video Lab: Falling Coffee Filters
Labs -
Video Lab: Two-Dimensional Projectile Motion
Resource Lesson:
RL -
Accelerated Motion: A Data Analysis Approach
RL -
Accelerated Motion: Velocity-Time Graphs
RL -
Analyzing SVA Graph Combinations
RL -
Average Velocity - A Calculus Approach
RL -
Chase Problems
RL -
Chase Problems: Projectiles
RL -
Comparing Constant Velocity Graphs of Position-Time & Velocity-Time
RL -
Constant Velocity: Position-Time Graphs
RL -
Constant Velocity: Velocity-Time Graphs
RL -
Derivation of the Kinematics Equations for Uniformly Accelerated Motion
RL -
Derivatives: Instantaneous vs Average Velocities
RL -
Directions: Flash Cards
RL -
Freefall: Horizontally Released Projectiles (2D-Motion)
RL -
Freefall: Projectiles Released at an Angle (2D-Motion)
RL -
Monkey and the Hunter
RL -
Summary: Graph Shapes for Constant Velocity
RL -
Summary: Graph Shapes for Uniformly Accelerated Motion
RL -
SVA: Slopes and Area Relationships
RL -
Vector Resultants: Average Velocity
Review:
REV -
Test #1: APC Review Sheet
Worksheet:
APP -
Hackensack
APP -
The Baseball Game
APP -
The Big Mac
APP -
The Cemetary
APP -
The Golf Game
APP -
The Spring Phling
CP -
2D Projectiles
CP -
Dropped From Rest
CP -
Freefall
CP -
Non-Accelerated and Accelerated Motion
CP -
Tossed Ball
CP -
Up and Down
NT -
Average Speed
NT -
Back-and-Forth
NT -
Crosswinds
NT -
Headwinds
NT -
Monkey Shooter
NT -
Pendulum
NT -
Projectile
WS -
Accelerated Motion: Analyzing Velocity-Time Graphs
WS -
Accelerated Motion: Graph Shape Patterns
WS -
Accelerated Motion: Practice with Data Analysis
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Advanced Properties of Freely Falling Bodies #3
WS -
Average Speed and Average Velocity
WS -
Average Speed Drill
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Chase Problems #1
WS -
Chase Problems #2
WS -
Chase Problems: Projectiles
WS -
Combining Kinematics and Dynamics
WS -
Constant Velocity: Converting Position and Velocity Graphs
WS -
Constant Velocity: Position-Time Graphs #1
WS -
Constant Velocity: Position-Time Graphs #2
WS -
Constant Velocity: Position-Time Graphs #3
WS -
Constant Velocity: Velocity-Time Graphs #1
WS -
Constant Velocity: Velocity-Time Graphs #2
WS -
Constant Velocity: Velocity-Time Graphs #3
WS -
Converting s-t and v-t Graphs
WS -
Energy Methods: More Practice with Projectiles
WS -
Energy Methods: Projectiles
WS -
Force vs Displacement Graphs
WS -
Freefall #1
WS -
Freefall #2
WS -
Freefall #3
WS -
Freefall #3 (Honors)
WS -
Horizontally Released Projectiles #1
WS -
Horizontally Released Projectiles #2
WS -
Kinematics Along With Work/Energy
WS -
Kinematics Equations #1
WS -
Kinematics Equations #2
WS -
Kinematics Equations #3: A Stop Light Story
WS -
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS -
Position-Time Graph "Story" Combinations
WS -
Projectiles Released at an Angle
WS -
Rotational Kinetic Energy
WS -
SVA Relationships #1
WS -
SVA Relationships #2
WS -
SVA Relationships #3
WS -
SVA Relationships #4
WS -
SVA Relationships #5
WS -
Work and Energy Practice: An Assortment of Situations
TB -
2A: Introduction to Motion
TB -
2B: Average Speed and Average Velocity
TB -
Antiderivatives and Kinematics Functions
TB -
Honors: Average Speed/Velocity
TB -
Kinematics Derivatives
TB -
Projectile Summary
TB -
Projectile Summary
TB -
Projectiles Mixed (Vertical and Horizontal Release)
TB -
Projectiles Released at an Angle
TB -
Set 3A: Projectiles
PhysicsLAB
Copyright © 1997-2017
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton