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Projectiles

Once off the ground, high jumpers are just like rocks...
What is a projectile?

An object launched into the sky and allowed to continue it's flight influenced only by gravity and it's own inertia is a projectile. On the moon, where there is no atmosphere, anything we launch into the sky is a projectile. There is no atmosphere on the moon to exert aerodynamic forces on a moving object.

The atmosphere on Earth changes things a bit. When something is moving relative to the surrounding atmosphere there is an aerodynamic force on the object.
  • If the aerodynamic force is very large relative to gravity and the inertia of the object, then we stop thinking of the object as a projectile. Airplanes, balloons, and cotton balls all fall into this category.
  • If the aerodynamic force is relatively modest, then we recognize the object as a projectile, but we account for the aerodynamic forces on it when estimating it's flight path. Cannon balls, meteors, and golf balls all fall into this category. 
  • if the aerodynamic force is very small, then we can safely ignore it. Bowling balls, high jumpers, and rocks all fall into this category.
Since high jumpers are the projectiles we are interested in, and since it is safe to ignore aerodynamic forces on high jumpers in flight, we will ignore aerodynamic forces from this point on.

The Path of a Projectile

The path of a projectile is characterized by:
  • Constant horizontal velocity. Once you leave the ground your velocity across the ground doesn't change. In other words, if the sun were directly overhead your shadow would travel across the ground at constant speed in the same direction you were going when you took off. This wouldn't change until you landed in the pit.
  • Constant acceleration downward. You leave the ground with upward speed, but as your flight progresses your ascent slows at a constant rate. This rate is called the acceleration of gravity (about -32 ft/sec2). When you reach the highest point of your jump, your vertical speed has been reduced to zero; you are no longer rising, but not yet falling. From that moment on, you begin to pick up downward speed as you continue to accelerate at -32 ft/sec2.

  • The arched (parabolic) flight path is the sum of the constant horizontal velocity and the constantly changing vertical velocity. The parabolic path of the jumper will seem rather narrow and a bit pointy if observed from behind the jumper or looking down the length of the bar. The true shape of the parabolic flight path can only be seen from a point along a line perpendicular to the flight path that runs through the high point (apex) of the flight.


Figure 1
Parabola
A high jumper's path through the air is a parabola: just like a rock. Both travel at a constant velocity across the ground, and accelerate downward due to gravity. This creates the arch-shaped path seen above. The graph shown above plots horizontal distance traveled vs. height.
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