# physics

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A hot-air 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.

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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

(M-m)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

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