Two particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity $g$ is uniform. If $u_1$ and $u_2$ be their initial speeds, then the time $t$ after which their velocities are mutually perpendicular is given by

  • A

    $\frac{\sqrt{u_1 u_2}}{g}$

  • B

    $\frac{\sqrt{u_1^2+u_2^2}}{g}$

  • C

    $\frac{\sqrt{u_1\left(u_1+u_2\right)}}{g}$

  • D

    $\frac{\sqrt{u_2\left(u_1+u_2\right)}}{g}$

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