What is the path length of a heat-seeking torpedo chasing an aircraft?

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The discussion revolves around calculating the path length of a heat-seeking torpedo as it chases an aircraft moving along the x-axis. The missile, initially positioned at a distance 'L' on the y-axis, continuously adjusts its trajectory to target the aircraft, which travels at a constant velocity 'u'. The missile's speed 'v' is greater than 'u', impacting the path length. Participants are encouraged to derive the general equation for the missile's trajectory. The conversation emphasizes the mathematical modeling of the scenario to find the solution.
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A missile and an aircraft are separated initially by a distance 'L' on the y axis. The aircraft starts moving along the x-axis with constant velocity 'u'. The missile is heat seeking which makes it point towards the aircraft at all times. The velocity of missile is 'v' where v > u. Find the length of the path of the missile and its general equation.
 
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