1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maximixe tunnel throughput

  1. Oct 5, 2014 #1
    1. The problem statement, all variables and given/known data
    historical data shows that between 15 and 35 mph, the space x between vehicles (in miles) is x = 0.324/(42.1 - v)
    where v is the vehicles speed in miles per hour

    Ignoring the length of individual vehicles, what speed will give the tunnel the largest volume in vehicles per hour?
    2. Relevant equations
    x = .324/(42.1-v)

    3. The attempt at a solution
    I thought I could set x = 0 (because spacing would be 0 ignoring the length of vehicles) and solve for v. That isn't correct.
    They show a solution where Q= cars/hour = (42.1v-v^2) / .324. I don't see where they get this.
    Then it looks like they take the derivative with respect to v of the numerator only and set it to next to 0
    dQ/dv = 0 = 42.1 -2v/.324 = 21.05 mph. This part makes sense to me but I still don't understand where they get Q = (42.1v - v^2)/.324.
     
  2. jcsd
  3. Oct 5, 2014 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    If you analyze the formula for the spacing of the vehicles, you will see there is no speed v which can make x = 0.

    From the data given about vehicle speeds and vehicle spacing, you've got to figure out how to determine the number of vehicles Q which enter the tunnel, as a function of vehicle speed, v. Once you have Q as a function of vehicle speed, then you can figure out which speed v gives the maximum Q.
     
  4. Oct 6, 2014 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    In case SteamKing's hint is not clear, there is a simple relationship between Q, v and x.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Maximixe tunnel throughput
Loading...