Height of ball bounce with air resistance

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]

[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

(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?


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