1. Limited time only! Sign up for a free 30min personal 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!

Related rates of a ladder sliding

  1. Nov 15, 2016 #1
    1. The problem statement, all variables and given/known data
    A 5 m ladder is sliding down the wall, and h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom at time t.
    Given that h(0) = 4 at t = 0 seconds and dh/dt = 1.2m/s, and the ladder is 5m long find x(2) and dx/dt at t=2 seconds

    2. Relevant equations
    x^2 + h^2 = 5^2
    25 - 16 = x^2
    x = 3

    3. The attempt at a solution
    $$2x*\frac{dx}{dt} + 2h*\frac{dh}{dt} = 0$$
    since we know that dh/dt = 1.2 and x = 3:
    $$2(3)*\frac{dx}{dt} + 2(4)*(1.2)= 0$$
    $$\frac{-9.6}{6} = \frac{dx}{dt}$$
    $$\frac{dx}{dt} = -1.6$$

    I believe dx/dt is -1.6 at t = 0 seconds, but how do I use this information to find x(2) and dx/dt at 2 seconds? Am I wrong in approaching this problem?
  2. jcsd
  3. Nov 15, 2016 #2


    Staff: Mentor

    In your problem statement, dh/dt appears to be constant at 1.2 m/s (really, this is -1.2 m/s). You're given that h(0) = 4, so what will h be at t = 2 sec.? From that you can find x(2).
  4. Nov 15, 2016 #3
    h(2) = 1.6m and x(2) = 4.73?

    Is my initial approach wrong though? And why is it that I got $$\frac{dx}{dt} = -1.6$$ which is the same coefficient of h(2)? I get that from a logical perspective this problem is very easy but I still want to do the math behind it.
  5. Nov 15, 2016 #4


    Staff: Mentor

    I don't get these values. dh/dt = -1.2 m/sec, and h(0) = 4. How did you get h(2) = 1.6 m?
    Last edited: Nov 16, 2016
  6. Nov 16, 2016 #5
    Realized my mistakes were because I wasnt' careful enough
    Okay so h(2) = 1.6m as 4-2(1.2) = 1.6
    then we can use that to find x(2):
    √(25-1.6^2) = 4.7377

    And then i input these values in to:

    $$\frac{dx}{dt} = \frac{3.84}{2(4.737)}$$

    and i get 0.405 for dx/dt.

    Edit: changed this post as the previous was wrong
    Last edited: Nov 16, 2016
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: Related rates of a ladder sliding