Final answer:
The question is about the principles of Physics related to gas laws and kinematics in the operation of a hot-air balloon and a dropped coin.
Step-by-step explanation:
The question pertains to Physics, which involves understanding motion, forces, and energy. Specifically, the question is about the behavior of gases under different conditions, Boyle's Law, and kinematics in the context of a hot-air balloon's operation and the dynamics of a dropped coin.
When a hot-air balloon is heated, the increase in temperature causes the air molecules to move more rapidly, striking the balloon's inner walls with greater force and resulting in increased pressure.
This is in accordance with the inverse relationship between pressure and volume for gases, as described by Boyle's Law, which becomes relevant as balloons expand or contract due to changes in atmospheric pressure at different altitudes. Additionally, kinematic equations must be used to calculate the motion of objects, such as a coin, released from the balloon.