Can we disprove this statement? How?

Asked by akshay2703 | 14th May, 2009, 04:48: PM

Expert Answer:

 Let us assume that the continious motion above has landmarks at points when achiles has travelled 100 m ,110 m,111 m etc. While solving the problem we have to keep in mind that we are shortening both our time frame as well as distance being covered during each subsequent landmark.

Consider following solution of the problem:

Let speed of achilles is 10 v and speed of tortoise is v. Let tis time when achilles is able to catch tortoise.

We have:

10vt=vt+100

t=100/9v

Clearly above time of approach is finite as v is non-zero.

Now in the given problem the solution has been framed in a different manner.

Time taken to reach first landmark, t'=100/10v=10/v

Time taken to reach second landmark is , t''=1/v

Total time taken forms a infinite series with solution,

t=t'+t''+t'''+ ...=10/v+1/v+1/10v+... =10/(1-1/10)v=100/9v

It is worth noting that in problem stated as above it is useful to remember that in a continious frame, difference between any two neighbouring values is infinite.

 

Answered by  | 31st May, 2009, 10:24: AM

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