Three assertions, Which are true? Which are false? Why? Options

[*mipadi*]

I'm going to make three assertions. Which of these are true, which are false, and why?

Assertion 1

Assume you have a cute little bunny rabbit, and you place her thirty feet away from a carrot. The bunny really wants the carrot, but she can only get to it by jumping halfway to the carry each time she hops. Clearly the poor bunny will never make it to the carrot, because the distance between her and the carrot can be divided in half an infinite number of times (i.e. no matter where she is, the distance left can always be divided in two).

Now assume that the bunny can move however she wants. She still will never reach the carrot, because to do so, she must move through the same points as in the previous example; but as noted, there are an infinite number of points to move through, which means the bunny can never, ever reach that carrot. In fact, to move at all, the bunny must move through an infinite number of points; so unfortunately, the bunny is rooted to whatever spot she starts out from. Poor bunny.

Assertion 2

I'm mad at you, and I throw a rock at your head. You run away and try to avoid the rock. But why even bother? Assume I throw the rock at you. Now, take note of the position of that rock at a single instance of time. It's not moving, is it? At a specific moment in time, the rock has a position, but it does not have time to move and so is at rest. During each instance of time, it is at rest for the same reason. Therefore, the rock is always at rest, and it never moves. Therefore, it is foolish for you to run away.

Assertion 3

Assume a tortoise and a sprinter race. The sprinter is a nice guy and knows he can beat the tortoise, so he lets the tortoise start a hundred feet ahead of him. The sprinter and tortoise then both begin the race and, upon reaching their maximum speed, continue running at that speed. Clearly the tortoise is much, much slower than the sprinter—but will the sprinter ever catch up to the tortoise? Unfortunately, the answer is no, he won't.

Assume the sprinter has run a hundred feet, and thus reached the tortoise's starting point. In this time, the tortoise has moved a foot, which still means he is beating the sprinter by a foot. The sprinter than runs another foot, catching up to the tortoise's position—or so it seems, but remember that the tortoise has moved during this period of time, too, so he is still a tiny bit ahead of the sprinter. The sprinter takes a tiny bit of time to reach this point, but in this period of time, the tortoise has moved forward a tiny bit more again. Thus, whenever the sprinter reaches a point where the tortoise has been, the tortoise has always moved a bit farther forward. No matter how fast the sprinter runs, the tortoise is always ahead. Wasn't he foolish for giving that tortoise a head start?!

[*wind&fire*]

false for the first one
where the rabbits' movement are classified as an "infinite geometric series"
e.g.
therefore to get to the carrot distances to get there would be
15+7.5+3.75+1.875...
this represents a infintie geometric series... there is a limiting sum as -1<r<1

S(initfinity) = times they have to jump

a = first jump = 15

r= ratio .5

S(initfinity) = a/(1-r)
= 15/(1-.5)
= 30
thus the rabbit must jump 30 times to reach the goal...(i hope its right... i havent done maths in 6 months)
----------------------------------
second one i think is false too as if we take into consideration the position of the rock being stationary therefore we must be stationary.. youve stopped time therefore were not moving either thus none of shall ever meet... if you examine the situation in instances then i would still be able dodge the rock since projectiles follow a predicatable parabolic path thus i would be able to shift as to miss the rock...
------------------------------------
im not sure wha the last one is since the end of the race was never specified and what constitutes as "race" ... here you assume being behind someone in a race is losing and were running in a loop...

This post has been edited by wind&fire: Mar 10 2006, 08:10 AM