Motion of a tiny tool thrown by an astronaut towards another astronaut inside a spinning space vehicle in a state of free fall revisited

A space vehicle rotating with a uniform angular velocity about a vertical axis fixed to it is falling freely vertically downwards, say, with its engine shut off. It carries two astronauts inside it. One astronaut throws a tiny tool towards the other astronaut. The motion of the tiny tool with reference to a rotating frame rigidly fixed to the space vehicle, i.e., relative to the astronauts, is considered. Second-order differential equations of its motion instead of fourth order 1] are obtained and are completely solved with exposure of a subtle method of solution, from pedagogic viewpoint utilizing the relevant initial conditions of its projection. Under certain conditions of projection of the tiny tool, it is established that it begins to float in the space inside the vehicle after describing an analytical maximum distance. The position and velocity of the tiny tool at any instant of time with reference to an inertial frame defined by the non-rotating frame initially coincident with the rotating frame at the time of projection of the tiny tool, are also found out. Finally two numerical examples are given.