Launch a projectile vertically
This page originally compiled Feb 2007 by TFR
We already have the tools we need to analyze this case. Neglecting the atmosphere, our projectile will simply proceed vertically up, uniformly decelerating at the rate g, until it comes to a stop relative to the ground, and then begin accelerating down at the rate g. We will be needing these sort of calculations to analyze our rocket as it begins its flight, lifting vertically from the launch pad before it begins to "pitch" over and head downrange.
Example:
We fire a projectile vertically out of a gun, at 1000 feet/second.
How high does it go, neglecting the atmosphere?
s = (vf2 - v02) / 2a = (02 - 10002) / (2 × -32.2) = 15528 feet
How long does that take?
t = (vf - v0)/a = (0 - 1000) / -32.2 = 31.1 seconds
and, of course, the projectile hits the ground at 1000 ft/sec at 62.2 seconds, under the assumption of no atmosphere.
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Last Revised: Feb 2007