Technology Reaper
Technology Reaper
How can the chicken cross the road … part 2?
Follow up to a previous question.
http://answers.yahoo.com/question/index;_ylt=AgfXikvmP7M3p5bg8dN43bTsy6IX;_ylv=3?qid=20070925065357AAV827T
A chicken crosses the road, the ends of which are defined by y=0 and y=10. The chicken starts at (99,0), and aims to end up anywhere on y=10. As the chicken begins to cross, the Grim Reaper is at the point (51,0) waiting to pounce. If the Reaper can intercept the chicken anywhere in y<10, the chicken is dead meat.
The Reaper has installed the following upgrades since the previous problem:
1) he is now waiting at the point (51,0) when the chicken begins to cross
2) he can instantly attain a top speed of 20 m/s in any direction
3) his tracking device is now equipped with stealth technology which allows him to predict the chicken’s path and adjust his pursuit strategy optimally.
What is the MINIMUM SPEED at which the chicken could cross in order to get over safely?
4.079 m/s is not the minimum.
I have acquired some experience in such problems already, so I propose the minimum to be exactly 4!
In my opinion the optimal strategy for the chick is to run from
(99, 0) to (99 + 2, 10) = (101, 10) because once again Dr D has chosen very carefully the numeric data. The whole problem is to find the meeting point, say P(x, 10) to minimize the ratio of both speeds v/20 (v - the chicken's speed), so apply little calculus and the function
v = 20*sqrt(((x - 48)² + 10²)/(x² + 10²)) for x >= 48 /initial distance/ has a local minimum at x = 50 and v_min = 4.
So, first time it was due North, now 10 to the North and
50 - 48 = 2 to the East and no chicken meat for the Reaper!
I'm waiting for the next upgrades of the evil Villain!
P.S.(EDIT) Greenduke: "Since the chicken ... her best strategy is to take the shortest path" - not necessarily - consider similar triangles (51,0), (101,0), (101,10) and (99,0), (99,10),(101,10), legs ratios 50:10 = 10:2!
Thanks for visiting!