# For the ballistic missile aimed to achieve the maximum range of 12500 km

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For the ballistic missile aimed to achieve the maximum range of 12500 km, what is the maximum altitude reached in the tra jectory?

x-motion: $12500000=vt$
​y-motion: $0=vt-\frac 12gt^2$
With v, one can find the maximum vertical height: $0-v^2=-2gh$.