Answer:
22.2 km
Explanation:
3397 km = 3397000m
Let gravitational constant [tex]G = 6.674\times10^{-11}m^3/kgs^2[/tex]. We can calculate the (constant) gravitational acceleration on this planet using Newton's gravitational law
[tex]a = G\frac{M}{R^2}[/tex]
where M and R are the mass and radius of the plannet, respectively
[tex]a = 6.674\times10^{-11}\frac{6.42\times10^{23}}{3397000^2} = 3.71 m/s^2[/tex]
When the bullet is travelling to its highest point, its kinetic energy is converted to potential energy:
[tex]E_p = E_k[/tex]
[tex]mah = mv^2/2[/tex]
where m is the bullet mass and h is the vertical distance traveled, v = 406 m/s is the bullet velocity at the firing point
We can divide both sides by m
[tex]ah = v^2/2[/tex]
[tex]h = \frac{v^2}{2a} = \frac{406^2}{2*3.71} = 22196.88m[/tex] or 22.2 km
