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; Wikipedia: Parabola: History). Probably, all those ballisticians who fired catapults, trebuchets, and early cannon NEVER thought of scientific idealization (air drag was always present in their empirical understanding), lack of doctrine of controlled experimentation, and lack of mathematical understanding of constant acceleration. 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.
Local file: local link: center_of_mass_fosbury_flop.html.
File: Mechanics file: center_of_mass_fosbury_flop.html.