A research balloon of total mass 240 kg is descending vertically with a downward

Question

A research balloon of total mass 240 kg is descending vertically with a downward acceleration of 3.8 m/s2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 2.4 m/s2, presuming that the upward lift of the balloon does not change.

Explanation / Answer

given initially it is moving down with acceleration of a=3.8m/s2 let the upward lift be F then mg-F=ma =>F=m(g-a)=240*(9.8-3.8)=1440N upward lift is 1440N let the mass thrown form the ballast be m then the total mass of the balloon=240-m and it should move upward with an acceleration of b=2.4m/s2 and the upward force is same so F-(240-m)g=(240-m)b =>F=(240-m)(g+b) =>m=240-(F/(g+b)) =>m=240-(1440/(9.8+2.4)) =>m=240- 118 =>m=122Kg so nearly 122 kg of mass should be thrown please lifesaver

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