How Much Ballast to Achieve Upward Acceleration?

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To achieve an upward acceleration of 1.3 m/s² for a 305 kg research balloon currently descending at 1.4 m/s², the net force acting on the balloon must be calculated. The initial downward force due to gravity is greater than the lift, resulting in a negative acceleration. To switch to upward acceleration, a specific amount of ballast must be removed to adjust the mass and change the net force. The discussion raises questions about the balloon's current acceleration and the necessary calculations to determine the correct amount of ballast needed. Understanding the forces and accelerations involved is crucial for solving the problem effectively.
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Homework Statement


A research balloon of total mass 305 kg is descending vertically with a downward acceleration of 1.4 m/s2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 1.3 m/s2, presuming that the upward lift of the balloon does not change.


Homework Equations


$$F=ma$$


The Attempt at a Solution


I'm having trouble because the original acceleration is positive and the final one is positive. How do I set up the proportion with what I have? Setting $$-305*1.4=m_2*1.3$$ doesn't work.
 
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