I think you will find everything you need to do this in the answers to yourOriginally Posted by asian5
earlier question here
RonL
....S o-----------------------+
.......|Y° *.............(sand)...|
..200|.......*.....................| 200
.......|............*................|
....A.+ - - - - - - - o - - - + B
.......|........a.........X *.......|
..200|........................*..Z°| 200
.......|...(mud).................* |
.......+-----------------------o F
........: - - - - 500m - - - - :
(please ignore the full stops)
details:
if the distance from S to F (hypotenuse) , passing through X =200(secY + sec Z)
and tanY + tanZ=5/2
and the distance from S to F, passing through X in terms of Y=200(secY + 0.5(4sec^2Y - 20tanY+25)^(1/2)
if an object can travel 4m/s through sand and 3m/s through mud, determine the best route it should travel through to get from S to F (hypotenuse), passing through X. and the time taken
Hello, asian5!
You don't need the angles to solve this part of the problem.
Code:S o-----------------------+ | * | 200 | * | 200 | * 500-x | A + - - - - - - - o - - - + B | x P * | 200 | * | 200 | * | +-----------------------o F : - - - - 500m - - - - :
If an object can travel 4m/s through sand and 3m/s through mud,
determine the best route it should travel to get from S to F,
passing through P, and the time taken.
Let , then
We have: .distance meters.
. . At 4 m/s, it will take: . seconds.
We have: .distance meters.
. . At 3 m/s, it will take: . seconds.
Hence, the total time is: .
. . . and that is the function you must minimize.
. . . . . . . . . . . Good luck!
Hello, Quick!
I think I've straightened out your format . . .
Soroban, I have already solved this problem.
If you see anything wrong with my work in the previous post, please tell me.
and the answer comes out to:
which can then be turned into (solving in terms of Y):
I missed your earlier post . . . I will take a look.