Acceleration

Let the mass of the balloon be , and the acceleration due to gravity be . The balloon is descending with an acceleration , so the net force on the balloon is: where is the tension in the string. Rearranging this, we get: Now, we need to remove mass from the balloon so that it starts moving upward with acceleration . The tension in the string should now be equal to the force required to accelerate the balloon upwards: where is the new mass of the balloon after mass is removed. Equating the tensions: Since we need the balloon to move upwards with acceleration , and , we can solve for . Substituting the values:
Thus, the mass that should be removed from the balloon is , which gives:
Thus, the correct answer is:

We need to use the equations of motion under uniform acceleration to solve this. The kinematic equation we will use is: where: - is the final velocity (8000 m/s), - is the initial velocity (2000 m/s), - is the acceleration, - is the distance traveled (4 m). Rearranging to solve for acceleration : Substituting the known values: - , - , - , Now, using the equation to solve for time : Substituting the known values: Thus, the time the particle spends in the tube is .