
Projectile Motion (Galileo and Newton)
General Description
This simulation presents two different views of projectile motion.
The first view, associated with Galileo, describes projectile motion
as a combination of horizontal motion with a constant velocity, equal
to the projectile initial horizontal velocity component, and
vertical motion with constant acceleration and an initial velocity
equal to the projectile's initial vertical velocity component. The second view,
described by Newton in his Principia, presents projectile
motion as a combination of inertial motion, with constant velocity
equal to the projectile's initial velocity, and motion produced by a
constant downward acceleration starting from rest. These two views
are mathematically equivalent, but each view emphasizes different
aspects of the motion.
The simulation shows the motion of the projectile for a given initial
height, launch speed, and launch angle (all of which can be selected
using the simulation controls). Optionally, the simulation
will display the velocity of the projectile, as well as the velocity
components (horizontal and vertical for the Galileo view, inertial and
forced for the Newton view). The simulation can also show a series of
"ghosts" - images showing the location and velocity of the projectile
at regular intervals of time. Finally, the simulation can display a
series of lines that illustrates how the two different types of motion
combine to produce the overall trajectory of the projectile.
By default the view is scaled to fit the entire trajectory, as well as
any ghosts, within the window. This generally means that the
horizontal and vertical distances are not shown to the same scale,
which can lead to distortions in the shape of the projectile and other
similar effects. The user has the option to square the display (see
below) to remove these effects, although this may result in the visual
elements occupying only a small portion of the viewing window.
Projectile Motion Frame
- Options Menu
- Show Lines: show lines illustrating how the two types of
motion combine to produce the overall trajectory.
- Show Ghosts: show images of the projectile and velocity
at regularly spaced time intervals.
- Show Velocity: show the velocity vectors for the
projectile and ghosts.
- Show Trace of Motion: show a trace of the projectile's
path.
- Show Red Elements: show elements illustrating the
vertical (Galileo) or forced (Newton) motion.
- Show Blue Elements: show elements illustrating the
horizontal (Galileo) or inertial (Newton) motion.
- Square Display: adjust the display so that the view is
the same size in the horizontal and vertical directions.
- Visual Elements
- Magenta filled circle: the projectile.
- Magenta open circles: projectile ghosts.
- Magenta trace: projectile's path.
- Black arrows: projectile and ghost velocities.
- Blue filled circle: projectile with horizontal (Galileo)
or inertial (Newton) motion only.
- Blue open circles: ghosts for horizontal/inertial
motion.
- Blue arrows: horizontal/inertial velocity components.
- Blue lines: illustrate displacement due to
horizontal/inertial motion.
- Red filled circle: projectile with vertical (Galileo)
or forced (Newton) motion only.
- Red open circles: ghosts for vertical/forced
motion.
- Red arrows: vertical/forced velocity components.
- Red lines: illustrate displacement due to
vertical/forced motion.
- Controls
- Buttons
- Play/Pause: start and stop the simulation.
- Step: advance the simulation by one time step.
- Erase: clear all traces.
- Initialize: initialize the simulation using current
parameters.
- Galileo/Newton: switch between Galileo and Newton views.
- Sliders
- Height: set initial height of projectile (in m).
- Speed: set launch speed (in m/s).
- Angle: set launch angle (in degrees).
Todd K. Timberlake (ttimberlake@berry.edu)