Assignment:
There is a rope that stretches from the top of Maidwell building to a tree on the racecourse, and the length of this rope is 1km. A worm begins to travel along the rope at the rate of 1cm each second in an attempt to get to the other end. then a strange thing happens...
Some malevolent deity intervenes to make life even harder for this poor little creature. every second (starting one second after the worm begins its journey) the rope is stretched so as to become 1 km longer. (So 0,1,2,3 seconds after the start the rope has length 1km, 2km,3km,4km, and so on.) In between these instantaneous stretchings the worm continues his 1cm per second crawll. The stretchings are uniform along the length of the rope, so there is a stretching of the distance of the worm from the start as well as a stretching of his distance from the far end. But each stretching maintains the proportion of the total that the worm has travelled.
So what happens? how far along the rope can the worm get? how long does it take him?
Provide complete and step by step solution for the question and show calculations and use formulas.