Projectile Motion
Relevant Physics:
The Independence of the Vertical and Horizontal directions means that a projectile motion problem consists of two independent parts:
* Vertical motion at a constant downward acceleration, which is equal to a = -g = -9.80 m/s2.
* Horizontal motion at a constant horizontal speed, vx = constant.

The object's vertical motion is the same as that of an object undergoing only vertical free-fall. Gravity only affects the object's vertical motion. Gravity cannot change the object's horizontal speed, and the component of the object's horizontal velocity remains constant throughout its motion.
Generic Equation of Frictionless Projectiles
Vertical Motion:
Constant Downward Acceleration


Horizontal Motion:
Constant Horizontal Speed


Total Space Motion:


Sketch
Projectile Motion QT Movie (460K)
The components of the velocity vector are shown for a ball tossed into the air at a fixed angle.

Information Implied:
When an object is propelled into the air, it is assumed that all other forces acting on the object except gravity are negligible. This means that:
* We neglect any effects due to air resistance on the object.
* We neglect any effects due to the Earth's rotation.
* The object does not rise high enough for the acceleration of gravity to change -- the body's acceleration is assumed to be both constant and downward regardless of its direction of motion or its height above the ground.
Frame of Reference:
* Projectile motion problems need a two dimensional coordinate system to describe the projectile's motion. The y-direction is usually associated with the vertical motion and location of the projectile, while the x-direction is usually associated with the horizontal motion and location of the projectile.* The generic equations for projectile motion assume the origin is at ground level, up is positive, right is positive, and that the clock starts the moment the projectile leaves the ground.
Analyzing a Projectile Motion Problem:
* Break the problem into two independent problems by resolving the velocity vector into vertical and horizontal components
* Solve the two problems independently.
* Recombine the resulting components, if needed, to determine the object's total space motion.
More examples of Projectile Motion Problem Solving.
Components of the Velocity Vector of a Projectile
A ball is tossed into the air on a parabolic arc. The components of the ball's velocity can be turned on or off. The magnitude and direction of the projectile's velocity can be changed by dragging velocity vector. Air resistance can also be turn on. Projectile Motion QT3 Movie (450K)
Student Target Experiment
A slow moving projectile is launched directly at a student hanging motionless by invisible skyhook. Having not done his home on freefall, he reasons that he should let go at the moment the projectile is launched so that he can drop out of its way. The simulation demonstrates that the projectile will always intersect the student's path under these conditions. The magnitude of the initial velocity of the projectile can be varied. as well as the student's initial distance and height from the launch point. Student Target QT Movie (248K)

Maximum Range for Elevated Launch
A ball is launched from the top of a building. The angle of launch can be varied to determine which angle will produce the maximum range.