Escape Speed and Energy Conservation

2021 1 question

1. 1 Gravitation Hard
   A particle of mass $m$ is projected with a velocity $v=kV_e$ ($k<1$) from the surface of the earth. ($V_e$ = escape velocity) The maximum height above the surface reached by the particle is:
   A $R\left(\frac{k}{1+k}\right)^2$ B $\frac{R^2k}{1+k}$ C $\frac{Rk^2}{1-k^2}$ D $R\left(\frac{k}{1-k}\right)^2$
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