# 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

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 $=18000+18000=36000m$