Hot Air Balloon Ride!
Introduction
Krishna and Sharky are out on a Hot-Air Balloon ride, and to their horrors, the balloon, instead of moving up with a speed of kmph, was moving down with the same. To make it move up with that speed, they need to reduce the weight.
Problem
The Hot Air Balloon has hot air filled in it, which gives it a constant upward force of Newtons and an air resistance, always working against the direction of velocity and directly proportional to the speed, acts on the Balloon. They want to reduce the weight, and Krishna suggests throwing their clothes off, which Sharky aggressively rejects with a bright idea.
'Let's Vomit!' yells Sharky to Krishna, 'It's the easiest and the safest way to reduce mass on the Balloon.' Krishna reluctantly agrees.
It so happens that Krishna drank a lot of water before coming, and so his vomit is dilute with a density of g/cc. And Sharky ate a wild bird in the morning, so the density of his vomit is g/cc.
Krishna and Sharky weigh and Kilograms respectively. They need to vomit so that their Balloon starts going up with the same velocity.
How many millilitres does Krishna vomit, given that Sharky vomits Litres.
Assumptions
The value of should be taken as and the Balloon has negligible mass. Any other assumptions which seem understood can be taken.
Extra Details
All the facts which appeared in this problem are correct. It was a tough task to find the densities of vomits of Krishna and Sharky.
The answer is 571.4.
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Force downward = (62.7+52)*10 = 1147 N & force upward = 1000 N
From the given information, we see theres a net force of -147 N on the balloon (minus sign implies direction). But if the balloon is to maintain constant velocity the net force should be 0. From this we can infer that the air resistance must be equal to +147 N @ -28 m/s & -147 N @ 28 m/s
Now since we want the balloon to go upwards at the speed 28 m/s, total force downwards needs to equal 1000N - 147N (the air resistance at 28m/s)= 853 N
Therefore we need to remove some weight form the balloon, which is partly achieved with sharky vomitting out 2.5*10 = 25 kilograms or 250N
so
This means Krishna will have to vomit 4.4/7.7 = 0.5714 L = 571.4 ml