To solve this problem it is necessary to apply the kinematic equations of movement description, specifically those that allow us to find speed and acceleration as a function of distance and not time.
Mathematically we have to
[tex]v_f^2-v_i^2 = 2ax[/tex]
Where,
[tex]v_{f,i} =[/tex] Final velocity and Initial velocity
a = Acceleration
x = Displacement
From the description given there is no final speed (since it reaches the maximum point) but there is a required initial speed that is contingent on traveling a certain distance under the effects of gravity
[tex]0 - v_i^2 = 2(9.8)(100*10^3)[/tex]
[tex]v_i = 14*10^2m/s[/tex]
Therefore the speed which must a rock thrown straight up is 14*10^2m/s to reach the edge of our atmosphere.
The displacement and gravity traveled are the same, therefore the final speed will be the same but in the opposite vector direction (towards the earth), that is [tex]14 * 10 ^ 2m / s[/tex]
