Posted by karim on Wednesday, March 2, 2011 at 3:10pm.
A hotair balloon of mass 200 kg is descending vertically with downward acceleration of magnitude 1.2 m/s2. How much mass (ballast) must be thrown out to give the balloon an upward acceleration of magnitude 1.2 m/s2 (same magnitude but opposite direction)? Assume that the upward force from the air (the lift) does not change because of the decrease in mass.

physics  drwls, Wednesday, March 2, 2011 at 5:30pm
Let B = the buoyancy force and M = the initial total mass. Let m be the ballast mass released
M g  B = M*1.2 m/s^2
(Mm)g B = M*1.2 m/s^2
Solve for m.
m g = M*2.4m/s^2
m/M = 2.4/g
m = 0.245 M = 49 kg