# 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]

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?

http://ift.tt/1kkY4g7

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