What Is the Fastest Descent Direction on Mt. Everest in a Snowstorm?

[wannabeengg]

1. While descending Mt. Everest you are caught in a sudden snowstorm. Unable to see more than a few feet in front of you, you determine through careful observation that if you travel three meters northwest you climb 1/2 meter, and if for every two meters you travel northeast you descend 1/4 meter.
1. In which direction should you start for fastest descent?
2. If you travel in this direction at two meters per second, what will be your rate of descend?
3. Derive an expression for your rate of descent as a function of the direction traveled and the speed in that direction.
4. In what direction should you go in order not to go up or down?I am having trouble in forming the functions.Kindly help

 

[tiny-tim]

welcome to pf!

hi wannabeengg! welcome to pf!

in questions like this, give the unknown a name, and then write out the equations

in this case, start by saying that the (steepest) slope is pointing θ west of north …

what do you get? ​

 

[wannabeengg]

Hello there, thanks for the kind welcome! i am not used to in other forums. Well my proffssor gave us a hint about using partial differentiation and also using the gradient vector. To find the steepest slope, we have to use ||the gradient of function f || or in other words the magnitude of gradient vector f. The main problem which i am having is about forming the function. I don't know what to do :-(

 

[tiny-tim]

hello wannabeengg!

(just got up :zzz: …)

the gradient is necessary if it's a complicated surface, but we can assume that this is a plane, so just draw a line of greatest slope, drop a perpendicular onto a horizontal plane, and use ordinary trig