Force and Air Balloon problem help

[Kinermatics]

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?

 

[Redbelly98]

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.)