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## Homework Statement

The problem describes an aircraft taking off from a point on a runway with constant speed [itex]V_{1}[/itex], climbing at a constant angle [itex]\alpha[/itex], at the point of takeoff, a car drives towards the aircraft a distance [itex]a[/itex] away with speed [itex]V_{2}[/itex]. I simply have to find the closest distance between the two objects

## The Attempt at a Solution

The x component of the distance is given by [itex](a-(V_{1}\cos(\alpha)+V_{2}))t[/itex]

The y component of the distance is given by [itex]V_{1}\sin(\alpha)[/itex]

Therefore the distance is given by [itex]\sqrt{((a-(V_{1}\cos(\alpha)+V_{2}))t)^2+(V_{2}\sin(\alpha))^2}[/itex]

Which I need to minimise, expanding the brackets and simplifying as much as I can gives the distance as:

[itex]\sqrt{a^2-2aV_{2}t-2aV_{1}t\cos(\alpha)+V_{1}^2t^2+V_{2}^2t^2+2V_{1}V_{2}t^2\cos(\alpha)}[/itex]

Kinda have no idea what to do next or if I even went in the right direction so any pointers would be great, thanks