FYKOS Year 27 Series 3 Problem 4 — I have already forgotten more than you ever knew · FYKOS 27 #27.3.4
Physics · mechanics · thermodynamics
Problem
A hot air balloon with its basket weighs M. The basket of the baloon is submerged into a water reservoir and water flows into it. Now we shall raise the temperature a bit and by that we raise the buoyant force acting on the balloon Mg+F. The basket has the shape of a rectangular cuboid with a square base which has a side of size a and is submerged into a depth H. The openings in the basket make up p≪1 of the whole area of the basket about which we assume that it is empty (with the exception of water). Let us neglect the viscosity of water and the volume of the basket itself. How quickly shall it rise depending on the depth of submersion?
Bonus: When shall it emerge?
Tip The expected speed of water flowing from the basket above the water surface is 2/3 of the maximum speed of water flowing out.