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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:
    F=-bv
    ma=-bv
    m(dv/dt)=-bv
    dv/v=-b(dt)/m
    [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
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