I cannot solve the problem of the ant on a rubber rope (Ant on a rubber rope - Wikipedia, the free encyclopedia)
in the case of a rope stretching exponentially:
the target end of the rope y(t) goes away exponentially
where D and H are positive constants. D is the initial length of the rope to be crossed by the ant.
Given that the rope stretches uniformly, I believe that the position of the ant on the rope x(t) should evolve according to
where c is the constant proper speed of the ant irrespective of rubber band stretching
initial condition x(0)=0
Can the ant reach the end of the rope depending on the relative values of c, D and H?
is it possible to prove that the ant will never reach the target, whatever the values of the constants?
or is it a critical point on the rope beyond which the target cannot be reached
many thanks in advance