Hopetoun Falls, Beech Forest, near Otway National Park, Victoria, Australia.
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Projectile motion images:
Projectile motion near the Earth's surface, neglecting air resistance, has a parabolic trajectory.
The only force acting is gravity.
Short trajectories of dense objects approximate parabolic motion pretty well because air resistance has a small effect.
Here's an animation of of a parabolic trajectory.
There are some illustratons from Galileo and his contemporaries Galileo's Analysis of Projectile Motion.
You many wonder why millennia past by and no one knew this.
Without fast photography or slow motion films, it's hard see to that the motion is nearly exactly parabolic.
Even so I think people---that is early physicists---couldn't have been all that observant.
Films did wonders for understanding for understanding everyday motions that were just a bit too quick for the human eye to analyze.
Well fast photography too---but fast photography implied films were possible.
Like horses galloping and buffalo running.
This may have been artistic licence, but it's factually incorrect and it may be that it just couldn't be figured out.
See e.g., cartoon.
Their feet are all off the ground when the legs close together.
Muybridge also has a fair claim to inventing many film genres: the sports film---that's clearly a jockey in the galloping horse clip---and the nature film (the bison)---because of the chaste nature of this course, we won't scroll down to the first skin flick.
You may not be able to see that projectile trajectories are exactly parabolic, but you can see that they approximately are.
But, of course, these are slow motion and snapshot examples.
But even so.
You can see the parabolic motion in balls rolling on inclines---which is how Galileo verified it if you allow for the facts that there are motions in 3 directions and the acceleration due to gravity is reduced by the incline and rolling effects.
Of course, it is the ballerinas's center of mass that follows a parabolic arc and because they are not rigid bodies the center of mass location changes relative to their body parts.
In fact, they spread their legs wider near the top, to raise their center of mass relative to their head and shoulders---but this tends to make their head and shoulders seem to follow a more horizontal than parabolic path---and gives the impression of flying along horizonatlly.
I'd demonstrate, but some of us have it and some of us don't.
In nature, it is probably most important for orbiting objects (see animation) which are often approximately in uniform circular motion---but, of course, can wildly deviate from it too.
In technology, almost all wheels make use of it at some time.