Hi MB2002,
Could it be useful to use polar coordinates, instead of cartesian ones? With the origin in the point where both turns start?
Thanks - Good lateral thinking. Relatively speaking we could use either aircraft as a frame of reference. At the point where both turns start, initially the aircraft are accelerating towards their respective centre of arc along a common line. (for a short period of time anyway)
acceleration (a) = V^2 * 1/R.
Plane A's a = V^2 * 1/10,000; Plane B's a = V^2 * 1/20,000.
Acceleration of A relative to B (a')= 2V^2 * 1/20,000 - V^2 * 1/20,000 = V^2 * 1/20,000.
Since both planes start at the same point and speed, their relative initial velocity = 0.
Therefore separation distance = 1/2 a' t^2.
Separation after 5 secs = 1/2 * V^2 * 1/20,000 * 25.
Dist = 111.3 feet Approximately.
V = 421.9 ft per sec (250 kts)