A rocket has iniistal mass 120kg and two-thirds of this mass is fuel. The air resistance force is given by F=-0.5v, where v is the velocity of the rocket. The rocket will be launched horizontally on frictionless rails from rest. While burning, the fuel is ejected at the rate of 0.8kg per second. The exhaust velocity of the fuel with respect to the rocket is 70 m/s. The rocket speeds up until the fuel is gone, then air resistance causes the rocket to slow back down. Find the times when the rocket is travelling at half of its maximum velocity. Note that there are two such times, one when the rocket is speeding up, and one when it is slowing back down.