Can you combine two accelerations together?

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Zynoakib
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When I was doing an exercise on projectile motion, there was a question that asked something like the max. altitude reached by an accelerating rocket. After some calculations, I got 23.96ms-2 as the vertical acceleration, then I minus it with 9.8ms-2 (gravitational acceleration as the two accelerations, I thought, should work against each other). Turns out, this is wrong and I should calculate the rest with 23.96ms-2 as the vertical acceleration. So my question is, why am I not supposed to minus 23.96 with 9.8? Because you can combine tangential acceleration and radial acceleration together to give a "resultant acceleration", but why is it not my case?

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I think you'll have to post the original question to get a clear reply. All that comes to mind is that gravity had already, in some way, been accounted for.
 
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