The problem of modelling the trajectory of an airplane that has begun to land and of optimally controlling the airplane until it touches the ground is considered in three dimensions. Two cost criteria are used. In the first case, the aim is to make the airplane touch the ground as close to a given target as possible, and as soon as possible. With the second cost criterion, we force the airplane to land inside a certain rectangle on the ground. In each case, the optimal control is obtained by considering the corresponding uncontrolled process.