Application of Differentiation Problem

  1. Here's a problem that I just found in my book and to my dismay, I couldn't figure out how differentiation can be used to solve a particular problem (seeing how we've just finished this unit at school). So here's the problem:

    Felicity and Jane start alking at the same time towards an intersection of two roads that meet at right angles.

    [​IMG]

    Felicity starts at 9km from the intersection while Jane starts at 13km from the intersection. Their speeds are 4 km/h and 3 km/h respectively. What is the closest that Felicity and Jane will get?

    I cannot figure out how to relate the two into one equation. Obviously, we need an equation for the distance between them and find the minimum for it (i.e. f'(x) = 0). Anyway, I thought I got differentiation down pat but ... guess not :frown:
     
    Last edited: Dec 9, 2006
  2. jcsd
  3. arildno

    arildno 12,015
    Science Advisor
    Homework Helper
    Gold Member

    Well, denote Felicity's position VECTOR as a function of time:
    [tex]\vec{r}_{F}(t)=(x_{F}(t),y_{F}(t))[/tex]
    and similarly, for Jane:
    [tex]\vec{r}_{J}(t)=(x_{J}(t),y_{J}(t))[/tex]

    now, choose an intelligent origin, specify the component functions, and find an expression for the distance between them, as a function of time.
     
  4. I haven't learned anything about vectors but I think I've got it. x = Felicity's distance to the intersection while y = Jane's distance to the intersection.

    [​IMG]

    So the closest they can get is 5 km :smile: Phew, haven't lost my touch yet. Thanks anyway arildno!

    Hmm I wonder why the images won't actually show up ...
     
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