# Max altitude of rocket [closed]

A rocket is launched perpendicularly with an initial acceleration of 10 m/s2, if the fuel runs out after 1 minute, what will be the maximum height reached by the rocket?

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## closed as off-topic by John Rennie, Qmechanic♦Mar 27 '14 at 11:16

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This problem is incomplete and cannot be solved. The information to determine how the acceleration varies is missing. – DarioP Mar 27 '14 at 9:16
@DarioP Agree, but I think the required information can be calculated. – Awal Garg Mar 27 '14 at 10:19
@AwalGarg You need at least the mass of the fuel and the mass of the empty rocket, then you may assume that the fuel is burned at a constant ratio and derive the acceleration as function of time. – DarioP Mar 27 '14 at 11:06

## 1 Answer

I assuming that the acceleration remains constant. So using Newton's equations- $$v=at$$ So after the fuel runs out, $$v=(10)(60)=600m/s$$ The distance it travelled in this time can be calculated by $$s=1/2at^2=(0.5)(10)(60)^2=18000m$$ Now, after the fuel runs out, the rocket will still go up a little bit, that can be calculated by- $$v^2-u^2=2gs$$ The $u$ here will be $v$ from the previous case and gravity is acting downwards and hence $g$ will be approximately $-10m/s^2$. So, $$s=-600^2/-20=18000m$$

Thus, Maximum Height $=18000+18000=36000m$

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Although this answer seems correct at the level of a school textbook, but how can you assume that acceleration remains constant? Isn't it constantly decreasing as the rocket goes upwards? – Awal Garg Mar 27 '14 at 10:18
I am pretty sure it's just a question for teaching school kids Newton's equations. Nothing wrong in assuming that the acceleration is constant. – Parth Vader Mar 27 '14 at 10:53
Initially I thought to consider a constant acceleration, but since the text of the problem say "an initial acceleration of" it is supposed to change, isn't it? – DarioP Mar 27 '14 at 11:00
Yeah that confused me too but I guess it is an error. I don't see any other way of solving this. – Parth Vader Mar 27 '14 at 11:05
I see another way of solving it. As we increase the altitude, gravitational acceleration decreases. Then, assuming constant acceleration provided due to the fuel's burning, total acceleration is provided by acceleration provided by fuel minus the gravitational acceleration. Thus, acceleration is changing. I think that is what's referred in the question by initial. – Awal Garg Mar 27 '14 at 13:02