- #1

- 2,257

- 7

This isnt homework but nobody is going to believe that so here it is:

at t=1 (or any nonzero value of t)

an ant starts moving across a balloon at velocity

how far does the ant move as a function of time?

the angular velocity of the ant is

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.

## Homework Statement

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?

## Homework Equations

## The Attempt at a Solution

the angular velocity of the ant is

ω(t) = v/r(t) = c/nct = 1/nt

integrating to get angular displacement I get θ(t)=log(t)/n

multiplying 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.

Last edited: