A hot air balloon of total mass M (including passengers and luggage) is moving with a downward acceleration of magnitude a. As it approaches a mountain, the captain needs to accelerate upwards. He decides to throw enough ballast overboard to achieve an upward acceleration of magnitude a/2. What fraction of the initial mass does he have to drop? Assume the upward lift force exerted by the air on the balloon does not change because of the decrease in mass.