To infinity and beyond!!!

lets say it reached till infinity...then it will have a min energy of MgR(potential energy).....so we'll give it before..as said by newton uncle in the form of K.E...so the answer

at infinity ,the total energy of the ball will become zero hence the sum of the potential energy n kinetic energy at earth is equal to zero i.e. GMm/2R + (-GMm/R)=0 AND g=Gm/R^2

Perhaps this will help.

The acceleration due to gravity: $g=\frac{G m_{\text{earth}}}{r_{\text{earth}}^2}$ .

$\text{Assuming}\left[(G|m|r|g)\in \mathbb{R}\land G>0\land m>0\land r>0\land g>0,G\ m_{\text{ball}}\ m_{\text{earth}}\ \int_{r_{\text{earth}}}^{\infty } \frac{1}{r^2} \, dr\right] \Rightarrow \frac{G\ m_{\text{ball}} m_{\text{earth}}}{r_{\text{earth}}}$

Does $g\ m_{\text{ball}}\ r_{\text{earth}}=\frac{G\ m_{\text{ball}} m_{\text{earth}}}{r_{\text{earth}}}$ ? It does.

We Know that Earth's Escape Velocity Ve=root (2gR) So from this we get the required Kinetic Energy= 1/2 x M x Ve^2=1/2 x M x 2gR= MgR

it is said that the ball is projected upwards so ,the initial force or acceleration is 0.so ,the body's acceleration is the gravity .

To escape any planets atmosphere an object require minimum velocity= (2gR)^1/2 so kinetic energyK.E.= 1/2 M 2gR=MgR