What happens to the body of a 3 year old when dropping her constantly from 6 foot tall father to 3 inch foam mattress topper on a bed for fun?
It depends on what you mean by constantly, and the exact height, the firmness of the bed, position of the child on landing, etc.
Fundamentally, the most problematic thing is happening in her head.
A man falling 30 feet hitting a concrete abutment will die of internal injuries, because while the outside of his body stops suddenly, the contents of the body cavities remain in motion (the inside of his body is still falling.) That means that things will rip loose inside his body (for example his right or left pulmonary artery will tear at the junction where they are first supported by underlying structures because his heart is still falling.) This is known as a deceleration injury.
The brain is particularly vulnerable to deceleration injuries, especially in babies. When your 3 year old hits the bed, everything inside of her jiggles a little bit on impact, including her brain.
This video shows the brain of an adult with a "coups/contrecoups" injury. It's dramatic because it's a car accident. But your 3 year old may be experiencing these types of injuries on a much, much smaller scale when she's dropped from a height onto a bed; it depends on many factors. And while a few times will most likely not hurt her in any way, multiplying this many times increases the chance of injury.
Bouncing is fun! That's why trampolines are fun. But the American Academy of Pediatrics discourages any use of trampolines, because of this kind of injury and others.
All kids jump on beds (under their own power), and mostly, he worst thing that happens is they fall off the bed and break an arm or something. As a mom who likes kids to have fun, I allowed my kids to jump on their beds. We (their dad and I) would also toss them in the air on a sheet, but note that the deceleration is much more gradual in that case.
As I said, a lot depends on various factors. Not knowing them all, I would advise against that activity just to be on the safe side.