A particle $A$ is projected vertically upwards. Another particle $B$ is projected at an angle of $45^{\circ}$. Both reach the same height. The ratio of the initial kinetic energy of $A$ to that of $B$ is

  • A

    $1 : 2$

  • B

    $2 : 1$

  • C

    $1\,\,:\,\,\sqrt 2 $

  • D

    $\sqrt 2 \,\,:\,\,1$

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  • [JEE MAIN 2023]