Originally Posted by

**Soroban**

The maximum height is: .$\displaystyle h\left(\frac{v_o}{9.8}\right) \;=\;v_o\left(\frac{v_o}{9.8}\right) - 4.9\left(\frac{v_o}{9.8}\right)^2 \;=\;\frac{v_o}{19.6}$ meters

Since the maximum height is 25 km = 25,000 m,

. . $\displaystyle \frac{v_o}{19.6} \:=\:25.000 \quad\Rightarrow\quad v_o \:=\:490,000\text{ m/sec}$

Therefore, the initial velocity is: .$\displaystyle \boxed{490\text{ km/sec}} $

There was a typo or something here.

Substitute into [1]: .$\displaystyle t \;=\;\frac{490,000}{9.8} \;=\;\boxed{50,000\text{ seconds}}$