On Christmas Day, a tiger leapt from its enclosure before killing a 17-year-old visitor to the San Francisco Zoo. In a new paper posted on the arXiv, a couple of enterprising Boston-based investigators tackle the basic physics problem implied by the incident:
Can a tiger overcome an obstacle that is thirty-three feet away and twelve and a half feet tall?
It’s a classic two-dimensional projectile motion problem – could a tiger, running at its maximum speed and launching itself at the right angle, clear the fence surrounding the enclosure? (You’d think the problem might have been worked out a little sooner...) In the paper, the authors helpfully connect their equations to the real world, like in this quip:
We begin by first writing down the two-dimensional kinematical equations satisfied by the projectile (tiger).
So can the cat clear the fence?
The authors work it out twice—once with calculus, once for the calculus-impaired:
From our calculations it was shown that a tiger only needs a little over 26 mi/hr to cross the 33 ft moat and clear the 12.5 ft high wall. From the current data that is available, a tiger can attain a maximum speed of 35 mi/hr. Hence, the current dimensions of the enclosure are not enough to ensure that a tiger will not escape.
The tiger only needed to be going at about 26 miles per hour if it hit the angle that minimized its required velocity, or about 55.4 degrees. A little more velocity would have given the feline a little more flexibility in terms of finding that perfect angle.
Yes, they found, the cat can fly.
Comments
neil says:
The "moat" was DRY!
The cat needed only
to run across it and
leep up the 12.5 ...
February 5, 2008 4:34 PM
vickie says:
I read the paper. The physics used is just basic projectile calculation, ok for a first cut. However, the assumptions are overly simplistic. How far does a tiger need to run to develop this speed? Tigers don't go from zero to 26 mph instantaneously. How strong do the tiger's legs have to be to overcome gravity for the height of this leap? Just because you can run a certain speed doesn't mean that you can propel yourself off the ground at this speed at any angle you desire. Clearly tigers don't hop out of enclosures every day, and the enclosure at the zoo held the tiger just fine for several years.
February 5, 2008 6:22 PM
Melissa says:
I'd be curious, if the original story i heard was true...how much did the tiger being shot at with sling-shots, figure into the equation?
February 5, 2008 9:44 PM
Richard says:
His center of gravity was probably two feed above the ground to start with, and he only had to get his front paws over the top of the fence to clear it by scrambling. At a 60 degree angle, and a distance of 5 or 6 feet from his center of gravety to his extended front paws, his vertical assent would only have to be 3 or 4 feet below the heignt of the wall for him to scramble over it.
February 5, 2008 10:03 PM
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