Force and Air Balloon problem help

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SUMMARY

The hot-air balloon problem involves calculating the fraction of weight a passenger must drop to change the balloon's acceleration from downward at g/3 to upward at g/2, given a constant lift force of 2Mg/3. The solution requires applying Newton's second law, F = ma, to determine the necessary adjustments in mass. The correct fraction of the total weight to be dropped is 5/9, which can be derived by analyzing the forces acting on the balloon and the resulting acceleration changes.

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Homework Statement


A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of g/3.

The passenger notices that he is heading straight for a waterfall and decides he needs to go up. What fraction of the total weight must he drop overboard so that the balloon accelerates upward at a rate of g/2? Assume that the upward lift force remains the same.

Lift Force = 2Mg/3

Homework Equations


F = ma


The Attempt at a Solution


I basically just tried to divide 2Mg/3 with g/2. But I just got M(4/3). The answer is 5/9. What critical information am I missing?
 
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Kinermatics said:

Homework Statement


A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of g/3.

The passenger notices that he is heading straight for a waterfall and decides he needs to go up. What fraction of the total weight must he drop overboard so that the balloon accelerates upward at a rate of g/2? Assume that the upward lift force remains the same.

Lift Force = 2Mg/3

Homework Equations


F = ma
To start, apply that equation to the situation where the balloon is accelerating downward at g/3. What do you get? (You might need to think carefully about what the F means in F=ma.)
 

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