This isnt homework but nobody is going to believe that so here it is: 1. The problem statement, all variables and given/known data at t=1 (or any nonzero value of t) an ant starts moving across a balloon at velocity v=c=1 (c is the speed of light)the radius of the balloon as a function of time is given by r(t)=nct (n is a constant much larger than 1) how far does the ant move as a function of time? 2. Relevant equations 3. The attempt at a solution the angular velocity of the ant is ω(t) = v/r(t) = c/nct = 1/ntintegrating to get angular displacement I get θ(t)=log(t)/nmultiplying by radius to get distance I get d(t) = r(t)*θ(t) = nct*log(t)/n = ct*log(t) The trouble is that this cant be right. if n>>1 then the ant can never get all the way around the balloon therefore the angular displacement θ must approach a limit as time goes to infinity. But log(t) increases without limit. I've gone over and over it it seems too simple to be wrong but it must be.