This is war!

Classical Mechanics Level 3

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

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