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LordGfcd

- 11

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## Homework Statement

A drop of water fall towards the ground with initial mass [m][/0] and radius [r][/0] (assume the initial shape of that water drop is sphere). the air resistance is F=½.ρ.A.[v][/2].C (C is the drag coefficent, A is the area that the air contact with the water drop and ρ is the specific weigh of the air). The bulk modulus of water is K, the atmospheric pressure is [p][/0], the gravitational acceleration is g. Assume the height was enough so the speed of the water drop can be constant at some point, find the formula that describe the shape of the water drop.

## Homework Equations

I think this is the most general problem.

## The Attempt at a Solution

I tried to consider a function in the Cartesian coordinate which the (0,0) point is the center of mass of that water drop. Apply the air resistant force on some dS area to the bulk modulus definition K=ρ.dP/dV but I can't somehow translate it to a differential equation form or even a dy/dx form to integrate. I don't think I did the math wrong. Is my way of approaching wrong ? My teacher said I can use another method using Larangian mechanic, the field I haven't studied throughout yet.

I will very appreciate if someone can tell me if my method is wrong there is a better approaching or if you attempted this problem before can you share with me your opinion. Thank you very much.

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