This is a problem for a fluid dynamics class I'm in. My current approach is to use a conservation of mass approach and say that the d/dt(momentum in the cart) = momentum into the cart. This leads to (u is speed of the cart, V is volume J is jet velocity, A is cross sectional area of the jet) d/dt(Vρu) = ρ dV/dt J where the left hand term represents the derivative of the current momentum of the cart, and the right hand term represents to momentum flux into the cart. I found that the rate at which water from the jet enters the cart will be dV/dt = A (J-u), i.e. the faster the cart is going the less water that actually enters it. Going back, and cancelling density, d/dt(Vu) = dV/dt J V' u + u' V = V' J, where prime is a time derivative. u' = V'(J-u)/V a = u' = A (J-u)^2/V but I cant proceed from here. Not only is the differential equation nonlinear, but the volume in the denominator will be an integral depending on u, V(t) = Vo + ∫(0 to t) V'(τ)dτ = Vo + A J t - A∫(0 to t) u(τ)dτ Since I couldn't solve it analytically I used numerical integration to get the u vs t curve and it looks as you'd suspect, with asymptotic behavior near u=J My question is whether or not there is a symbolic answer, and if so how is it obtained?