If a body of mass \(100\) kg is thrown vertically upwards from the surface of the earth with a velocity equal to
\[
\frac23
\]
times its escape velocity, then the maximum height reached by the body is
\[
(\text{Radius of the earth}=6400\text{ km})
\]
Show Hint
Use conservation of mechanical energy:
\[
\boxed{
\frac12mu^2-\frac{GMm}{R}
=
-\frac{GMm}{R+h}.
}
\]
Also,
\[
\boxed{
v_e=\sqrt{\frac{2GM}{R}}.
}
\]