Final answer:
The maximum height a rocket can achieve is likely with a half-filled 2-liter bottle, as it offers a balance between propellant volume and air pressure space. Rocket design considerations, like amount of propellant and bottle size, are crucial in determining altitude capability.
Step-by-step explanation:
The maximum height a rocket can achieve depends on a combination of factors including the amount of propellant and the bottle size that holds the propellant. In this context, when comparing the given options, the half-filled 2-liter bottle may provide the best combination for maximum height. This is due to the fact that the 2-liter bottle has sufficient volume to hold a larger amount of propellant (water and air in the case of a water rocket), while still allowing adequate space for pressurized air. A half-filled bottle gives a balance between the amount of water for thrust and the air pressure that can be built up for ejection. The three-quarters filled 1-liter bottle may not allow enough air space for adequate pressure build-up. A full 0.5-liter bottle lacks enough propellant to reach high altitudes. Without additional information on the design of the rocket, the materials used, and the launch mechanism involved, the exact maximum height cannot be determined definitively; however, based on basic principles, the half-filled 2-liter bottle is a strong candidate for achieving the greatest altitude.
In rocket design, factors such as the amount of propellant, bottle size, and air pressure all play significant roles in determining the maximum height achievable. Therefore, it is important to consider the balance between these factors when attempting to reach the highest altitude possible with a bottle rocket.