Here is the context of the problem:
Calculate the size of the iron meteor that would have its initial velocity reduced by only 10% by
drag in Earthís atmosphere.
I was able to prove the first part:
Write down a differential equation for the deceleration of the meteor du/dt.
However have no idea about the next:
You should find an equation of the form du/dt = . . ., where the stuff on the RHS depends
only on the density of air (which depends on height in the atmosphere z), the
internal density of the meteor, the radius of the meteor, the meteorís velocity, and dimensionless
constants. You can assume (check, if you like) that the extra acceleration
provided by gravity over this distance is negligible, since the meteorís velocity is already
Convert your equation to a linear, first-order differential equation. That is, you should
have an equation which reads something like dy/dz = f (z)y, where f (z) is some function
of z. (Hint: begin by noting that dt = dz/v, and substitute y = v2.)
Solve this equation, imposing boundary conditions as appropriate. (You will probably
end up using an integrating factor.)
Hence, calculate the critical radius and mass of the meteorite such that the velocity at
z = 0 is 0.9 times the initial velocity.