Final answer:
The question explores the concept of maximum distance in various physical contexts, such as projectile motion, thermal physics, and cosmology. It requires applying physics principles to calculate distances that objects, substances, or light can reach.
Step-by-step explanation:
The question pertains to the maximum distance that various objects or substances can reach under different circumstances. This is a physical concept often associated with projectiles, thermal expansion, or light in the context of the universe's expansion. In the case of a battleship cannon, for example, the maximum distance a shell can be fired involves calculations of initial velocity and projectile motion, taking into consideration factors such as the Earth's curvature. In thermal physics, water density reaches a maximum at a certain temperature due to molecular motion and hydrogen bonding, which has implications for the behavior of water in different environments, like ice-covered lakes.
For the problem about the horizon distance in the context of the Big Bang model, the maximum distance refers to the furthest point light could have traveled since the universe began, highlighting the limitation of observable space. Each of these scenarios involves complex physics principles and mathematical calculations to determine the maximum distance achievable.