A fighter plane is flying horizontally at a height of $250\  m$ from ground with constant velocity of $500\  m/s$. It passes exactly over a cannon which can fire a shell at any time in any direction with a speed of  $100\  m/s$. Find the duration of time  for which the plane is in danger of being hit by a cannon shell

  • A

    $2\sqrt 3\ sec$

  • B

    $\frac{5}{{\sqrt 2 }}\ sec$

  • C

    $3\sqrt 2\ sec$

  • D

    $2\sqrt 2\ sec$

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