How can the chicken cross the road … without falling into the deadly embrace of the Grim Reaper? - chicken
A chicken crossing the road while the Grim Reaper on his motorcycle noise about his death.
The sides of the road are from the x-axis (y = 0 defined) and the line y = 10 meters. The chicken crossed with a constant speed of 2 m / s, the developed (99.0) and is aimed at all y = 10 end.
Meanwhile, the chicken starts to cross, be brought death to the origin (0,0) and 20 m / s along the axis X of your bike with a tracking device that can directly lead Reaper, provided the position of the pelvis any point in time to keep a speed of 20 m / s.
The Grim Reaper is required by law is only the slaughter of chickens and \\ \\ \\ \\ \\ \\ \\ \\ u0026lt 10th How did the chicken cross the road without risking death?
Tuesday, December 8, 2009
Chicken How Can The Chicken Cross The Road … Without Falling Into The Deadly Embrace Of The Grim Reaper?
7 comments:
Yes, you can survive the poor animal runs directly north to the point (99, 10)! The rules require that the villain will be saved for orientation of the victim and, at the time "t" 2t victims would be north of the starting point and if Y = Y (x) is the equation of the curve continuing villain, the distance
20 t = ∫ [0, x] sqrt (1 + y ²) dx, where
/ Dx = sqrt (1 dt ² + y ') / 20, instead of the velocity vector has the bad direction of the tangent to y = Y (x), which this tangent intersects the x-axis in the x - y / y'. To these measures to the point of contact, have the X-axis and the vertical lines ξ ξ = x = 99 we are 2 similar right triangles, as follows:
2. / Y = (99 - (x - y / y'))/( x - (x - y / y ')) or
2t = y + (99 - x) y ', differentiation
dt / dx = y "(99 - x) / 2, so for the prosecution and the curve y = (x), we have the differential equations of 2nd order:
and "(99 - x) / 2 = sqrt (1 + y ² ') / 20, or
and "(99 - x) = sqrt (1 + y ² ') / 10, the initial conditions:
and (0) = 0, y '(0) = 0 / DO in.int - Origin Executive - East /. Solve by substitution z = y, we obtain:
∫ dz / sqrt (1 + z ²)) = (1 / 10) ∫ dx / (99 - x) + constant, or
Income (z + sqrt (1 + z ²))*( 1 - x/99) ^ (1 / 10) = 1, back to z = y '
2y '= (1 - x/99) ^ (-1/10) - (1 - x/99) ^ (1 / 10) and finally
y = 45 (1 - x/99) ^ (11/10) - 55 (1 - x/99) ^ (9 / 10) + 10
This is the equation of the path of evil. Taking x = 99 here and we get (99) = 10, then the villain and the victim are being developed (99, 10) After exactly 99 * 20 / (20 ² - 2 ²) = 5 seconds, but under the rules of hunting today
y = 10, then evil can only cry in despair.
I bow before the victims!
PS (Edit - after reading the answers above) and David Emmet right directly on the optimal strategy Chicken - Running to the north, but the explanations are not satisfactory: the way the prosecution is indeed a curve, so that the position of the 1. Reaper second is not (20, 0). Neither in the second to 5 (99.83, 5.03), by the calculations of the Emmet / I cINSURANCE an't read Yahoo Answers cut / are wrong, the final position is exactly (99, 10) and the ratio of 20:2 is the heart of this problem - the chicken is not if your is weak.
In general, all data for this problem will be chosen really nice and interesting to match the optimal strategy.
We can speed the mower at all times with the system of equations Vx = 20cos find tan [-1 (Py (c) / 99)]
Tan Vy = 20sin [-1 (Py (c) / 99)]
where Py (c) is the position and chicken
Then you can find the equation for the position of the mower, with the integral of each side of 0 when it reaches the chicken y = 10 ... 10/Vy IU (c)
Px (g) = (int tan 20cos [-1 (Py (c) / 99)], t, 0, 10/Py (c))
Py (g) = (int tan 20sin [-1 (Py (c) / 99)], t, 0, 10/Py (c))
The solution of this solution, which is definitely for speeds of differance to cross safely the chicken cross the road when you have a straight line. Chickens are in (99.10), while the mower (99.83,5.03). Chickens are in a V (c) between 1.01 and 2 meters per second secure. Performance analysis with the Pickers can homing device and its extraordinary speed, may not be able to catch the chicken into several courses, because overshooting.errors (Note in this example the line of the mower already crossed the chicken in the x Direction ..;).
We can speed the mower at all times with the system of equations Vx = 20cos find tan [-1 (Py (c) / 99)]
Tan Vy = 20sin [-1 (Py (c) / 99)]
where Py (c) is the position and chicken
Then you can find the equation for the position of the mower, with the integral of each side of 0 when it reaches the chicken y = 10 ... 10/Vy IU (c)
Px (g) = (int tan 20cos [-1 (Py (c) / 99)], t, 0, 10/Py (c))
Py (g) = (int tan 20sin [-1 (Py (c) / 99)], t, 0, 10/Py (c))
The solution of this solution, which is definitely for speeds of differance to cross safely the chicken cross the road when you have a straight line. Chickens are in (99.10), while the mower (99.83,5.03). Chickens are in a V (c) between 1.01 and 2 meters per second secure. Performance analysis with the Pickers can homing device and its extraordinary speed, may not be able to catch the chicken into several courses, because overshooting.errors (Note in this example the line of the mower already crossed the chicken in the x Direction ..;).
Just a question to see if I understand the tracking device.
If the path is just north of the chicken, the path of the mower, the hypotenuse of a triangle that is formed the distance of the chicken and the horizontal axis. Is that correct? Thank you.
Chickens could go without getting destroyed. I think I felt the presence of the distance traveled per second. If so, the chicken did not drive safely in 5 seconds.
Taking note of 5 seconds, I thought, the reaper, (0,0), go to (20.0) in the first second of its objective, the chicken at y = 0
2. ) For the second (a little awkward grammar, the case was about to change. I have provided a triangle that would be the reaper in (20.0) y = 2 is already the chicken's face. So I have 79 for the length (from chicken to 29, less Reaper 20) and height 2
I used to) the tangent angle of 79 neighboring units along the sides of the triangle, tan (angle) = 2 (compared to the reference angle) / 9 (adjacent side of the angle resolved reference.
I have an angle of about 1.45
With this angle and a hypotenuse of 20 years, I have an x-value of about 19.99 and there is a value of 0.5.
per second into the second 5, the harvester would that change its angle relative to P in PoolOyster.
for 2 up to 5 seconds, I had the angle
2 sec - 1.45 degrees
3 sec - 1.94
4 sec - 2.93
5 s - 12.52
Well, if you combine the distance traveled by the form of x, 5 seconds to calculate, it would be approximately x = 100 But do not worry, the chicken! There is still the component of the reaper ...
per second and progressive values of 1, 2, 3, 4, 5 0, 5, 67, 1.02 and 4.3
When the chicken is safe, and 5 seconds (99.10), the harvester would only y = 6.49. The chicken has already risen.
I believe it is prudent to assume, that the second calculation per second would be even, because needed in less than 1 second, the angle changes accordingly ...
I think ...
Since chickens can fly, and motorcycles in general not, then I think that adding a "z" axis is the dilemma of the chicken to solve ...
Things! No, it can grimreaper met people as if we care if a chick! Now just starting to sweep them off the table as a liar anyway.
Post a Comment