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Parabolic ramp problem.

  1. Nov 26, 2015 #1
    1. The problem statement, all variables and given/known data

    Let's say that a ramp is modelled using the equation y = cx2, where c is a constant. Assuming a motorcycle starts at speed vi, displacement xi=0 and launches off the ramp at a horizontal displacement of xf, what is the motorcyclists speed and direction?

    2. Relevant equations

    y = cx2
    gradient = m = tan(θ)
    F = gsin(θ)
    F = ma

    3. The attempt at a solution
    The gradient at each point, x, is given by:
    dy/dx = m = 2cx

    For an inclined plane, m = tan(θ), so from above:
    tan(θ) = 2cx
    θ = tan-1(2cx)

    The force down the slope at any point is F = gsin(θ), so:
    F = gsin(tan-1(2cx)) = (2cxg)/√(1+4x2)
    a = F/m = (2cxg)/(m√(1+4x2))

    V = ∫adt, but the acceleration is in terms of x so I'm not sure what to do... I obviously need to find a way to link the displacement to the velocity, but I'm not sure how.
     
  2. jcsd
  3. Nov 26, 2015 #2

    haruspex

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    Hint: You don't need to deal with forces and accelerations.
     
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