Height of ball bounce with air resistance

[ajuric]

Homework Statement

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:

$F_r = \frac{1}{2} c S ρ v^2$

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

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

(Ans: $h = 9.15 m$)

Homework Equations

Given above.

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?

 

[rude man]

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.