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!

Homework Help: Deriving a Velocity Equation

  1. May 17, 2010 #1
    1. The problem statement, all variables and given/known data
    The Pitt Fall is thrill ride at Kennywood that lifts passengers to a certain height, pauses for a few moments, and then drops the riders, causing them to free fall towards the ground before gradually applying breaks 79 ft above the ground. Assume there is a drag force, F=-bv, and the terminal velocity reached is 65 mph (29.1m/s). There are 16 passengers, each weighing 178 lbs, and the ride weighs 10,000 lbs. Determine the value of b. Derive the velocity equation as a function of time.

    2. Relevant equations
    I understand that you must use calculus, but I do not know how to derive the equation.

    3. The attempt at a solution
    I found that b=1962.6, and I started to derive the equation, but I am not certain where to go from here:
    [tex]\int dv/v[/tex]=-b/m[tex]\int dt[/tex]
  2. jcsd
  3. May 17, 2010 #2
    First you got value of b wrong i guess. And net force on the ride its not just -bv, there is gravity too, otherwise this whole ride would have no meaning ;] Net force is F = mg - bv (if you choose your positive axis downward)
    Terminal velocity means that F=ma=0 (a = 0) so velocity does not change: mg - bv =0 -> b = mg/v (use right units too - if g is in m/s^2, then v in m/s)
    As for finding v in terms of time, just write:
    F = ma = m(dv/dt) = mg - bv
    Last edited: May 17, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook