A light plane (mass = M) makes an emergency landing on a short runway. With its engine off, it lands at speed v0. A hook on the plane snags a cable attached to a sandbag (mass = m) and drags the sandbag along. The coefficient of friction between the sandbag and the runway is μ, and the plane's brakes give a retarding force of Fb. How far will the plane go before it stops?
Data: v0 = 43.0 m/s; M = 839 kg; m = 97 kg; μ = 0.32; Fb = 1208 N.
The Attempt at a Solution
Im pretty sure these are the correct forces, however, the solution to the diff eq does not yield a function (i.e. e^-(something) that goes to zero) that will give a stopping point. My thought is I am missing a part of the equation or have to incorporate momentum.