$($b$)$ A rocket sled has an initial mass $4$ metric tons, including $1$ ton of fuel. The motion resistance in the track on which the sled rides and that of the air total kU $,$ where k is $75N.\frac{s}{m},$ and U is the speed of the sled in $\frac{m}{s}.$ The exit speed of the exhaust gas relative to the rocket is $1500\frac{m}{s},$ and the exit pressure is atomsphere. The rocket burns fuel at the rate of $90k\frac{g}{s}.$ Compute the speed of the sled after $10$ s $.$