Caption: The net external force determines the motion of the center of mass of a body per Newton's 2nd law of motion (AKA F=ma). However, internal motions can relocate the center of mass relative to the various parts of the body. Recall a center of mass is the mass-weighted average position of body.

In the image, the high jumper (doing a Fosbury flop) clears the bar, but NOT his center of mass---he wiggles over the bar. The center of mass follows a parabolic trajectory as dictated by Newton's 2nd law of motion (AKA F=ma) and gravity. This happens to any thrown object if air drag is negligible. For millennia, no one understood this---even though it's obvious from jet fountains.

So why do you need to know about center of mass? To clear the bar.

High jumping is like being in orbit---once you leave the ground, your center of mass has to go with gravity.

Parabolic trajectory videos (i.e., Parabolic trajectory videos):

1. Parabolic motion Range of a projectile | 0:31: In the ideal limit when air drag is zero, objects near the Earth's surface follow exact parabolic trajectories (i.e., y=a-bx**2 paths with "a" and "b" positive). The launch ballistics elevation 45° gives the maximum range as the video shows. Good for the classroom.
2. How To Do A Basic Somersault | 1:59, jumps to 0:45: Once the gymnastist has left the ground, their center of mass must follow a parabolic trajectory no matter what their internal motions are. When gravity is the only external force, it dictates that the center of mass motion is a parabolic trajectory. Just show a few seconds. Good for the classroom---but don't try this at home.
3. Juggling Club Passing 20180513 002 | 0:39: Similarly, the juggling club centers of mass follow parabolic trajectories no matter how they are rotating during juggling passing. Just show a few seconds. Good for the classroom.
4. New Style Swimming Pool Decoration Led Lighted Jumping Jet Fountain | 0:10: For two thousand years at least since the ancient Roman fountains, humankind has known jet fountains whereby you can just see a frozen parabolic trajectory, but it took Galileo (1564--1642) to discover parabolic trajectory for projectile motion near the Earth's surface (see Wikipedia: Galileo Galilei Scientific methods). Good for the classroom.
5. Dick Fosbury Changes The High Jump Forever - Fosbury Flop- Mexico 1968 Olympics | 0:32: Dick Fosbury (1947--2023) at the 1968 Summer Olympics, Mexico City. Dick Fosbury did NOT invent the Fosbury flop, but he perfected it and brought it to high-level sports competition (see Wikipedia: Fosbury flop). Notice the folks just lounging under beach umbrellas---they're having a long day under the bright Sun in Mexico City at elevation ∼ 2000 m. Good for the classroom.

Credit/Permission: © User:AlanSiegrist, 2016 / Creative Commons CC BY-SA 4.0.
Image link: Wikimedia Commons: File:Fosbury Flop English.gif.
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File: Mechanics file: center_of_mass_fosbury_flop.html.