Projectile motion

1. Sep 17, 2008

timloser1987

1. The problem statement, all variables and given/known data

A rock is launched vertically.
During the last second of the flight, the rock covers one-half of the entire distance covered during the entire flight. What is the maximum possible duration of the flight?

Hint: Answer $\neq 2 s$

2. Relevant equations

Consider 1-D motion:

When the rock is moving upwards,

$$-(mg+b\dot{y})=m\ddot{y}$$.

When the rock is falling,

$$-(c\dot{y}-mg)=m\ddot{y}$$

3. The attempt at a solution

I've solved for the velocity and displacement functions but somehow I kept getting 2 seconds as my answer. The question isn't very explicit in stating what you should consider, but I assumed it to be air resistance that is directly proportional to the velocity $R=-kv$. Intuitively it would appear that for any air resistance in order to maximize the duration of the flight the resistance constant $k$ will have to be zero. But somehow it just doesn't work that way.

Is there something wrong with my assumption that air resistance is proportional to $v$ and not $v^{2}$, since I've also learned that it can be proportional to the square of the velocity, too.

Some guy suggested that this can be modelled such that the gravitational force is non-constant, i.e. use $F_{g}=\frac{Gm_{1}m_{2}}{r^2}$, but I have no idea how to solve that way.