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Height of ball bounce with air resistance

  1. Apr 13, 2014 #1
    1. The problem statement, all variables and given/known data
    Ball with mass of 0.7 kg and radius 0.15 m is dropped from top of the building 30 m tall. Force of air resistance which acts on ball is given with the equation:

    [itex] F_r = \frac{1}{2} c S ρ v^2 [/itex]

    where
    [itex]c = 0.5[/itex]
    [itex]S = r^2 ∏[/itex]
    [itex]ρ = 1.29 \frac{kg}{m^3}[/itex]
    [itex]v = current speed. [/itex]

    How tall will ball bounce of the ground if we suppose that collision was
    elastic?

    (Ans: [itex] h = 9.15 m [/itex])

    2. Relevant equations
    Given above.

    3. The attempt at a solution
    I have solved this with differential equations of motions(which took me quite a lot
    of time integrating...) but I'm interested whether this can be solved with equations
    for kinematic and potential energy and how?
     
    Last edited: Apr 13, 2014
  2. jcsd
  3. Apr 13, 2014 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    I don't think so, since energy dissipated by air friction is a function of v and you don't know v unless you solve the diff. eq.
     
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