Calculus question!!! see below...?
A dune buggy is on a straight desert road, 40 km north of Dustin City. The
vehicle can travel at 45 km/h off the road and 75 km/h on the road. The
driver wants to get to Gulch City, 50 km east of Dustin by another straight
road, in the shortest possible time. Determine the route he should take.
- M3Lv 710 years agoFavorite Answer
.. |\ angle ACP = z.
..A. x P ...B gulch city
...<---- y --->
let dist. to dustin city = w (40 km)
speed ratio regular road: desert road = k (5/3)
dist. over desert = w•sec z,
dist. over regular road = y - w•tan z
time taken ∞ k•sec z +(y - 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 = 40/√((5/3)^2 - 1)
ans: x = 30 km
note that the optimal value of angle z is solely dependent on k !
- stollsteimerLv 45 years ago
Its (eleven+five)/(eleven+15) =sixteen/26 = sixty one.538% roughly. (Note: I'm assuming that it entails those who're freshman "and" feminine. So, if thats now not the case, my reply is flawed then. Sorry.)