Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Related rates question pls help

  1. Mar 22, 2008 #1
    A sailor in a boat 10 km off a straight coastline wants to reach a point 20km along the coast in the shortest possible time. Toward what point on the shore should he head if he can row at 4 km/h and run at 12 km/h?

    i believe this involves optomizeation as well ralated rates but i am unsure as to how to get the equasion to maximize.

    sailor ---------- | (straight coast)
    dx/dt=4 km/h |
    | y= 20 km dy/dt= 12 km/h
  2. jcsd
  3. Mar 22, 2008 #2
    srry guys, i tried to make a picture at the bottom. I didnt know it wouldn't permit the spaces i input.
  4. Mar 22, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Let x=0 be the point on the coast directly fronting the boat.

    Call the unknown point at the coas for X.

    Then, the time it takes for him to reach X by the boat is [itex]\frac{\sqrt{10^{2}+X^{2}}}{4}[/itex]
    and the time for him to reach his destination after that [itex]\frac{20-X} {12}[/itex]
    Thus, his total time T(X) is given by:
    [tex]T(X) =\frac{\sqrt{10^{2}+X^{2}}}{4}+\frac{20-X} {12}[/tex]
    Do you agree with this?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Related rates question Date
B I need help with a related rates question Jul 24, 2016
I Related Rates (+Trig) Question Apr 10, 2016
Related Rates Question Oct 19, 2010
When calculus fails Related rates question Feb 15, 2010
Related Rates questions Jan 22, 2005