Question

A hot air balloon takes off from the edge of a plateau. The balloon travels through the air along the parabolic path given by the function f(x) = -4/2500x² + 4/5x.

Answer 1

A hot air balloon moves smoothly in the air due to the principles of buoyancy and temperature difference. The warm air inside the balloon is less dense than the atmospheric air, creating a buoyant force that allows the balloon to rise and stay afloat.

Step-by-step explanation:

A hot air balloon moves smoothly in the air due to the principles of buoyancy and temperature difference.

First, the balloon is filled with hot air by burning a propane burner, which heats up the air inside the balloon. The warm air is less dense than the surrounding atmospheric air, creating a buoyant force that lifts the balloon.

This buoyant force allows the balloon to move smoothly in the air, as it is able to generate lift and stay afloat. The pilot controls the altitude of the balloon by adjusting the temperature inside the balloon, which affects the buoyant force. By adding more or less heat, the pilot can make the balloon ascend or descend.