1. The problem statement, all variables and given/known data An empty bucket (mass M, area A) is launched with velocity v0 from a space station into a cloud of dust (density ρ). As the bucket moves through the dust it will collect dust in it until the bucket comes to a stop. Solve the place of the bucket x=x(t). 2. The attempt at a solution Okay. Here is my attempt to solve this. momentum of the bucket dp = v*dm + dv*m. As a particle of dust with mass dm collides with the bucket its momentum changes by u*dm, where u=-v is the change of the velocity of the particle. On the other hand the change in momentum of the particle has to be the same as the change in momentum of the bucket. So... dp = u*dm = -v*dm 2*v*dm+m*dv=0 1/v*dv = -2/m*dm Let's integrate v=v0...v, m=M..m ln(v0/v) = -2*ln(m/M) ---> v = v0*(M/m) On the other hand mass of the bucket M will change by m(x) = M + A*ρ*x where x is the length of travelled distance. and this coupled with the equation of velocity we get. dx/dt = v0*(1+ρ*A*x/M)^-2 v0*dt = (1+ρ*A*x/M)^2 * dx Lets integrate again t=0..t x=0..x and we get v0*t = x + k*x^2 + 1/3*k^2*x^3 where k=ρ*A/M Now by solving x, which I'm not going to do here, we get x=x(t) Have I done this right? Is there simplier way to do this?