(a) if I start 10 meters behind who will win, and by how much?
(b) if I start 11 meters behind who will win, and by how much?
(c) if I start 11.1 meters behind who will win, and by how much?
(d) what is furthest I could start behind, and still win?
Explain your answers.
Lets assume that we are both world class sprinters.
You run the 100 meters in a time of 10 seconds flat, giving you a speed of 10meters per second (m/ps).
I run 90 meters in the 10 seconds giving me a speed of 9 m/ps
(a)
You run 110 meters at a speed of 10m/ps...taking 11 seconds to finish the race.
I run 100 meters ar a speed of 9m/ps...taking 11.11 seconds to finish the race.
In 11 seconds I cover 99 meters (9*11)....you win by 1 meter, or by 0.11 seconds when I cross the finish line.
(b)
You run 111 meters at a speed of 10m/ps...taking 11.1 seconds to finish the race.
I run 100 meters ar a speed of 9m/ps...taking 11.111...seconds to finish the race.
In 11.1 seconds I cover 99.9 meters (9*11.1)....You win by 10 centimeters, or by 0.0111 seconds when I cross the finish line.
(c)
What is the furthest behind you can start and still win the race.?
If you start 11.11 meters benhind me, you will win the race by 1 centimeter or by 0.00111 seconds.
If you start 11.111 meters behind me, you will win the race by 1 millemeter, or by 0.000111 seconds.
Theoretically we could continue this progression of to an infintesimal detail, but it is after all a foot race and at some point it would be declared a dead heat. the timing systems in use today for sprints only time to 1/100 of a second, so you starting at 11.11meters behind would result in a time of 11.11 meters for both sprinters and be declared a photo finish... the results of this photo would then show that you won because of your big nose.....
so my answer to (c) is 11.11 meters.
Now if I were to break your nose just prior to the race, breaking it sideways so that it was 10mm shorter..........would the camera be able to show that you won by a bloodclot on the end of your nose?