system
Given the following post, respond as if you're commenting on Reddit:
human
What is the ideal mass for a ball so it can be thrown the furthest distance?

So, this is something I've been wondering for a while now. If I were to throw a really heavy ball, it would barely go anywhere, because I can't throw it very fast. If I were to throw a really light ball, it would also not go very far, because air resistance would stop it quickly. Something like a tennis ball seems like an ideal mass between these two extremes. So I ask, what is the ideal mass to make a thrown object travel the longest distance.

To define the situation more precisely, there is a ball of radius R (you choose) at ground level. It is given kinetic energy E and launched at an angle of 45 degrees. When it hits the ground again, it stops. What mass maximizes the distance?
gpt
IMHO you need to add some basic assumptions: A human, when throwing an object of moderate weight (lets say, lighter than 150g), is primarily limited by *speed*, not projectile energy: You won't be able to throw a 10g projectile significantly faster than you could throw a 150g projectile.

So the ideal projectile should be throwable (near) top-speed, but be as heavy as possible (exact weight depends on human anatomy and throwing technique).

Empirical evidence suggests that 45m/s is a pretty hard-to-break limit for ~150g, baseball-shaped projectiles- no significant improvements of this speed have been achieved in the last 20 years.