Nine lives are flashing before their eyes

Unfortunately, cats fall out of windows in cities sometimes. In a famous article, The New York Times notes that the likelihood that a cat survives a fall goes down as the fall distance increases (expected) but then goes back up at very large distances (perhaps unexpected). If the statistics are correct, then there should be some physical reason this occurs. Some have suggested that terminal velocity and cat biology come into play. The article above indicates that cats have a terminal velocity of 60 miles per hour (mph). If we model the drag force FdF_d on a cat as

Fd=12kAv2F_d=\frac {1} {2} k A v^2

where AA is the cross-sectional area of the cat, vv is its velocity and k=1 kg/m3k = 1 \text{ kg/m}^3, what is the cross-sectional area in m2\mbox{m}^2 of a 5 kg5 \text{ kg} cat with a terminal velocity of 60 mph60 \text{ mph}?

Details and assumptions

  • The acceleration of gravity is 9.8 m/s2-9.8~\mbox{m/s}^2

  • 1 mile=1.6 km 1 \text{ mile} = 1.6 \text{ km}


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