A particle is projected with velocity $\mathrm{k}{\mathrm{v}}_{\mathrm{e}}$ in the vertically upward direction from the ground into space (${\mathrm{v}}_{\mathrm{e}}$ is escape velocity and $\mathrm{k}<1$). The maximum height from the centre of the earth to which it can reach is

• A

  $\frac{\mathrm{R}}{{\mathrm{k}}^2+1}$
• B

  $\frac{{\mathrm{k}}^2\mathrm{R}}{1-{\mathrm{k}}^2}$
• Correct answer
  C

  $\frac{\mathrm{R}}{1-{\mathrm{k}}^2}$
• D

  $\frac{{\mathrm{k}}^2\mathrm{R}}{{\mathrm{k}}^2+1}$

Hence, the correct answer is option: 'C'.