Projectile with air resistance

[nrqed]

oh i see now. my differential equation skills are not too great. So i now integrate both sides?

Sorry, I had left a factor of "m" on the left side which should not have been there.

You can't integrate since v(t) is an unknown function. The fact that it is squared makes this a nonlinear equation which is tough. I am trying to guess the solution but I don't see it right away, sorry.
(maybe Maple could give you the answer).

 

[Jess1986]

thanks, you have still helped me get on the right track. once i find v do you know where i should go from there?

 

[nrqed]

thanks, you have still helped me get on the right track. once i find v do you know where i should go from there?

In principle, here is what you have to do:

Sokve for v(t) with the initial condition v(0) = U.

set v(t)= 0 to find the time to get to the highest point.

Integrate v(t) to find y(t) (with the initial condition y(0)= 0). Plug in the time from the first part to find the max height reached.

Now start again, but now solving dv/dt = +g - k v^2 with the initial condition v(o) = 0.

Integrate v(t) to find y(t) with the initial condition being the max height.

Find the time at which y is zero again.

Plug back that time in the formula for v(t) on the way down.

It's that easy

 

[Jess1986]

thanks very much for all your help. il give solving the equation in maple a go tomorrow and see how it goes!