Rockets

Two rockets have the same speed v. The original distance is L. At the
beginning, one is moving perpendicularly to the line segment between the two
rockets, and its speed and direction is unchanged. The other is always
aiming at the first one. So, what is the final distance of these two rockets
?


Assume the B is purchasing A. A is moving to direction of x+.
x(A), x(B) is the x coordinates of A and B.
we can see the fact that x(A)-x(B) + |AB| = constant.
At beginning, x(A)-x(B) = 0, |AB| = L
At the end, x(A)-x(B) = |AB| = L/2.


is there a trivial way to show that x(A)-x(B) + |AB| = constant?


d|AB|/dt = v cos theta - v
d(xa -xb) /dt = v - v cos theta

theta is the angle between AB and x direction.

The distance between two airplanes A and B is a at time 0. Plane A flying  north at speed v, and plane B will fly toward A at the same speed v. What is the trajectory of B?

y'=dy/dx=(vt-y)/x
and
\int_x^a \sqrt{1+y'^2} dx = vt

Solvable.