Irodov Problem 1.104

The body will first decelerate in its upwards journey and come to a complete stop in the air. It will then begin to fall down and experience air drag. We will consider both these situations separately.

Upward journey:
There are two forces acting on the body, i) the force of gravity mg and ii) the air drag which acts downwards in order to oppose the body's upward motion. In other words both gravity and air drag oppose the body's upwards motion. So we have,














The maximum height achieved by the body is given by (1).

Downward journey
After achieving its maximum height the body begins its decent. During decent, gravity accelerates the body downwards, but the air drag acts upwards trying to oppose the body's downward motion. Thus we have,














From (1) and (2) we have,