This is war!

A fighter plane is flying horizontally at a height of 250 m from ground with a constant velocity of 500 m/s. It passes exactly over a low-powered missile launcher which can fire a missile 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 the missile in seconds.

Assumptions and Details

• Gravitational field strength at Earth's surface is 10 $m/s^2$

• The missile is not self-propelled