Problem statement: A Helium filled balloon has a volume of 1 cubic meter and a mass of 0.200 kilograms. It is released and rises through the air because of its buoyancy. The buoyant force is equal to the weight of air displaced by the balloon.. This force is given by: F_b = [1.29e^(-1.21h)]g, where h is the altitude in km. 1) Draw a free body diagram and calculate the net force on the balloon at h=0. 2) Determine the altitude, h, at which the net force is zero.. 3) Using the mass of the balloon and the expression for the buoyant force, derive an expression for the net force on the balloon as a function of altitude, h. 4) Get an expression for the velocity as a function of height by using: dv = adt = a(dt/dh) dh (Note that this is not constant acceleration, you need to integrate.) 5) At what height does the balloon stop moving upward? Relevant equations: f_net = ma f_g = mg v = integral of [a] dt Attempt at solution: 1) F_b at (h = 0) = 12.65N F_g = mg = .2*9.81=1.96N F_net = 12.65-1.96=10.69N 2) F_net = 0 when F_b = F_g h=1.54 km 3) F_net = F_b-mg = 9.81[1.29e^(-1.21h)]-.2(9.81) 4) F_net = ma a = F_net/m = (1.29e^(-1.21h)g-mg)/m v = 9.81[(-1.29e^(-1.21h))/(.2*-1.21) – h] 5) v=0 when: 9.81[(-1.29e^(-1.21h))/(.2*-1.21) – h] = 0 h=1.21922 km I am not too sure of my answer for #4. And also, what is troubling me is why the balloon will stop moving at 1.21922 km but the net force will not be zero until 1.54 km?