Power Line Optimization QUestion? (calculus)?? HELP URGENT!?
A man lives on an island 1 km from the mainland. His favorite pub is 3 km along the shore from the point on the shore closest to the island. The man can paddle his canoe at 3 km/h and can jog at 5 km/h. Determine where he should land so as to reach the pub in the shortest possible time.
I really don't understand it. PLZ HELP! it would be greatly appreciated!!
- M3Lv 71 decade agoFavorite Answer
.. C island
.. |\ angle ACP = z.
..A. x P ...B pub
...<---- l --->
let speed ratio land:water = k (5/3)
dist. over water = w•sec z,
dist. over land = l - w•tan z
time taken ∞ k•sec z +(l - tan z)
dT/dz = k•secz•tan z - sec^2 z
= (ksin z - 1) / cos^2 z
for minima, sin z = 1/k
which yields x = w /√(k^2 - 1)
x = 1/√((5/3)^2 - 1)
ans: 0.75 km
- 4 years ago
the better proper nook is at (x, 5-x^2) the better left nook is at (-x, 5-x^2) so the width is 2x the height is 5-x^2 So the area is wh = 10x - 2x^3 take the deriv and set to 0 10 = 6x^2 x^2 = 10/6 = 5/2 clean up for x about a million.fifty 8 height = 5-x^2: calculate and multiply for section