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This question already has an answer here:

I have a model rocket I'm planning to launch. I heard from someone that you can calculate the altitude by timing the rocket from the time it takes off to the time it lands. Does anyone know how to do this?

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marked as duplicate by Floris, John Duffield, Sebastian Riese, Gert, ACuriousMind Nov 26 '15 at 0:49

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  • $\begingroup$ There's a huge amount of information missing to be able to solve that problem even approximately. $\endgroup$ – Gert Nov 25 '15 at 19:16
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    $\begingroup$ Possible duplicate of Rocket Altitude Calculation $\endgroup$ – Floris Nov 25 '15 at 19:44
  • $\begingroup$ I marked this as a duplicate of a question which shows what other information is needed, and how you can go about solving the problem you are asking about. $\endgroup$ – Floris Nov 25 '15 at 19:45
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You can decouple the horizontal and vertical motion of your rocket. In the vertical direction you have vertical thrust and gravity and horizontally you only have thrust (I ignore air resistance here). As you are interested in the altitude only, we only look at the vertical problem. All kinetic energy in the vertical direction is converted to potential energy so that your rocket reaches a height $h$.

$E_\text{kin}=E_\text{grav}$

$\tfrac{1}{2}mv^2=mgh$

$\tfrac{1}{2}v^2=gh$

Since the acceleration is constant, you have $v=at=gt$ and we find that the height equals

$\tfrac{1}{2}gt^2=h$

Since your rocket travels both up and down and since the path is symmetric around the apogee, you can calculate your altitude by

$h=\tfrac{1}{8}g\Delta t^2$,

where $\Delta t$ is the time between launch and landing.

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  • $\begingroup$ This only works for ballistic rather than powered motion (so the engine has to explode instantly on the launchpad) and also only if air resistance is ignored (so at the very least the rocket can't use a parachute to land). $\endgroup$ – user10851 Nov 25 '15 at 18:49
  • $\begingroup$ That formula is pretty useless for actual rockets although it works for a vertically fired shell, assuming you accurately know the muzzle velocity. A rocket's kinetic energy continues to increase as long as it's thrust overcomes $mg$. Work is done during flight, not just a launch. $\endgroup$ – Gert Nov 25 '15 at 19:15
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Did model rocketry for a while... from a practical standpoint this isn't feasible... unless you're talking about deploying something that drops at a rate you know at the time of the parachute deploying (like a weighted streamer. See the link below). Your chute deploys and you don't know the descent rate of it, so there's no way to find the vertical distance.

However, a more practical thing is to track the path of the rocket upwards, from a distance away from the base (say, 400 feet, maybe more for a more powerful rocket). Use a clinometer to track the angle the rocket flies up and record the maximum angle. From there, use trigonometry to find max height.

http://www.hobbizine.com/rocketaltitude.html

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