The hot air balloon inventor is widely credited to be the Montgolfier brothers, Joseph-Michel and Jacques-Étienne, who successfully launched the first untethered manned flight in a hot air balloon in 1783. Their invention revolutionized the way humans could travel through the air and paved the way for modern aviation. The brothers' pioneering work in hot air balloon technology laid the foundation for the development of air travel and aeronautics as we know it today. **

A hot air balloon rises when filled with hot air because hot air is less dense than cold air. When the air inside the balloon is heated, it becomes less dense and lighter than the surrounding cooler air. This difference in density creates a buoyant force that causes the balloon to rise. As the balloon continues to be heated, the air inside becomes even lighter, causing the balloon to ascend further. **

A hot air balloon rises because of the principle of buoyancy. The air inside the balloon is heated, which makes it less dense than the surrounding cooler air. This difference in density creates an upward force, known as buoyancy, that lifts the balloon off the ground. As long as the air inside the balloon remains hotter than the air outside, the balloon will continue to rise. **

A hot air balloon works by heating the air inside the balloon envelope, which causes it to become less dense than the surrounding air. This creates lift, allowing the balloon to rise. The burner at the base of the balloon heats the air, and as it rises, the balloon is carried along by the wind. The pilot can control the altitude of the balloon by adjusting the temperature of the air inside the envelope. **

Yes, a balloon rises with hot air because hot air is less dense than cold air. When the air inside the balloon is heated, it becomes less dense than the surrounding air, causing the balloon to rise. This principle is used in hot air balloons, where a burner heats the air inside the balloon to make it rise. **

A hot air balloon ride is a truly magical and breathtaking experience. The feeling of floating gently through the sky, with panoramic views of the landscape below, is incredibly beautiful and serene. The colors of the sunrise or sunset reflecting off the balloon and the peacefulness of the experience make it a truly unforgettable and awe-inspiring adventure. **

Both gas balloon aircraft and hot air balloons fly due to the principle of buoyancy. In the case of a gas balloon aircraft, it is filled with a lighter-than-air gas, such as helium or hydrogen, which creates a lifting force that allows it to float in the air. On the other hand, a hot air balloon uses heated air inside the balloon to create a lower density inside the balloon compared to the surrounding air, resulting in a lifting force that allows it to ascend. In both cases, the buoyant force overcomes the weight of the aircraft, allowing it to fly. **

No, one cannot perform calculus with a hot air balloon. Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities. It involves concepts such as derivatives and integrals, which are not related to the operation or mechanics of a hot air balloon. Calculus is a mathematical tool used to solve problems in various fields such as physics, engineering, and economics, but it does not have any direct application to the operation of a hot air balloon. **