Will the Bug Ever Reach the End of the Stretching Rubber Band?

[Satvik Pandey]

Suppose if the bug would have started walking from the end of the rubber band which is in our hand to end which is attached to wall? Will it reach the other end of the rubber band?
Assuming that other conditions of question remains same.

 

[Orodruin]

Suppose if the bug would have started walking from the end of the rubber band which is in our hand to end which is attached to wall? Will it reach the other end of the rubber band?
Assuming that other conditions of question remains same.

What are your thoughts?

 

[Satvik Pandey]

What are your thoughts?

I think that bug will reach the other end of the band.
I think relative velocity of bug w.r.t Earth at any point $x$ (measured from the wall)
is $u-\frac { xv }{ L+vt }$.

 

[D H]

\frac{dy}{dt}=\frac{\dot x}{L+vt}-\frac{xv}{(L+vt)^2}

(With initial value y=0 when t=0)
Which could be written as:

\frac{dy}{dt}=\frac{\dot x-yv}{L+vt}

(I got stuck here for a few minutes but then thought of this )
Maybe I should plug in \dot x=u+vy and then I get:

\frac{dy}{dt}=\frac{u}{L+vt}

Excellent! This is what I wanted you to do way back in post #7. It's such a simple result that it's hard to give a hint (other than try it, it's easy!) that doesn't tell the answer.