Calculating Maximum Height of Object Thrown Upward

[Yann]

I don't know much about classical physics, if I throw a rock or mass M upward with an initial velocity Z, with gravity g and air resistance A acting against it, is this equation the right one ;

\(\displaystyle m\frac{dv}{dt} = (Z-g)m -Av\)

Then if I want to know the maximal height, I just need to integrate v(t) to find the distance at time t. Right ?

I'm really not sure about this equation, mostly because of the (Z-g) term. After all, it's about INITIAL velocity.

 

[mgb_phys]

You have to define what you mean by air resistance 'A', is this a force or a drag coefficent, is it a function of V or a constant?
Generally the equation you want is s = ut + 1/2 gt^2

See the formulae sticky thread for more equations.

 

[nicktacik]

If you define air resistance to be a force proportional to the velocity

Then the forces on it as it's going up are mg down and Av down, so you get

$$\frac{dv}{dt} = -g - \frac{Av}{m}$$

You then have to solve this differential equation for v(t), using v(0) = Z as a boundary condition. Then you have all the information you need about the rock's movement.