Final answer:
A hot air balloon has three degrees of freedom and moves by the principle of buoyancy, rising when the air inside it is heated. The balloon's altitude is controlled by adjusting the air temperature inside, and pilots use varying wind directions for steering.
Step-by-step explanation:
A hot air balloon has three degrees of freedom in movement: vertical translation (up and down), and two horizontal translations (forwards and backward, left and right). The motion of a hot air balloon is governed by buoyant force, which causes it to rise when the air inside is heated and becomes less dense than the surrounding cool air.
The pressure of the gas in a hot air balloon at rest is equal to the pressure of the outside atmosphere, as per the initial conditions described.
However, when a hot-air balloon's burner is fired and heats the air inside, the pressure momentarily increases until the air expands and the pressure equalizes. Through this process, combined with the fact that hot air is less dense, the balloon rises due to the buoyant force acting upon it.
Hot air balloons can move smoothly in the air because of this controlled buoyancy. To control altitude, the temperature inside the balloon is regulated by the burner. Pilots can take advantage of different wind directions at various altitudes to steer the balloon indirectly.