It is desired to use a hot air balloon with a volume of \(320,000 \mathrm{ft}^{3}\) for rides planned in summer morning hours when the air temperature is about \(48^{\circ} \mathrm{F}\). The torch will warm the air inside the balloon to a temperature of \(160^{\circ} \mathrm{F}\). Both inside and outside pressures will be "standard" (14.7 psia). How much mass can be carried by the balloon (basket, fuel, passengers, personal items, and the component of the balloon itself ) if neutral buoyancy is to be assured? What mass can be carried by the balloon to ensure vertical takeoff acceleration of \(2.5 \mathrm{ft} / \mathrm{s}^{2}\) ? For this, consider that both balloon and inside air have to be accelerated, as well as some of the surrounding air (to make way for the balloon). The rule of thumb is that the total mass subject to acceleration is the mass of the balloon, all its appurtenances, and twice its volume of air. Given that the volume of hot air is fixed during the flight, what can the balloonists do when they want to go down?