As far as meaty physics goes, The Bourne Ultimatum is a standout among action flicks. Compared with other pillars of the genre, like Mission Impossible and XXX, Bourne sustains some impressive dramatic excitement without succumbing to the patently ridiculous.
It's not hard to suspend disbelief during the movie's dizzying quick cuts, but Jason Bourne's Superman-like physical capabilities are a little suspect. He has astonishing reaction reflexes, infinite physical stamina, and the ability to withstand an amazing quantity of forceful blows, impacts and collisions without sustaining much more than a few scratches and an intermittently gimpy leg—pretty unlikely stuff, even for an elite assassin.
But we're not here to criticize the improbable. Why else do we go to action movies, after all? That said, there is one interesting physics moment that I feel obligated to point out: a motorcycle chase scene in which Bourne tries to prevent a CIA assassin from snuffing out the closest thing he has to a romantic interest. While taking a short cut, Bourne jumps his motorcycle over what appears to be a six-foot concrete wall. Fans of XXX may not bat an eye—Vin Diesel's grasshopper-esque, unassisted leaps over a 30-foot fence, a guard tower and a house, all without the assistance of a ramp of any kind, make Bourne's paltry six-footer look like a bunny hop. Nevertheless, it's worth taking a look at the numbers. Just how much force must he be capable of exerting on the ground to get him over the wall?
First, a little kinematics. Assuming he leaps just high enough to make it over, he'll have zero vertical velocity at the top of his trajectory. We can then calculate the initial speed with which he must have left the ground:
V2 - V02 = 2aΔy,
where V is the vertical velocity at the top (zero), V0 is the vertical velocity upon launch, a is the acceleration due to gravity and Δy is about six feet, or two meters. Solving for V0 we get:
V = (2(9.8m/s2)(2m))1/2 = 6.3 m/s.
Now let’s consider that a typical jump involves about 0.2 seconds of contact time with the ground. From this we can calculate Bourne’s upward acceleration when he pushes off:
a = Δv/Δt = 6.3 m/s/0.2 s = 32 m/s2.
Applying Newton's Second Law we can now estimate how much force he will have to apply to do this. (And don’t forget Newton's Third Law: However hard he pushes down into the ground, the ground will push back up with an equal force.)
Fnet = Fpush – mg = ma,
where Fpush is the force the ground exerts upward on Jason and his relatively small motorcycle and mg is their combined weight. Let's assume that his futuristic bike is super-light at 100 kg, and he himself is a trim but solid 80 kg.
Fpush = mg + ma = 180kg (9.8m/s2) + 180kg (32m/s2) = 7600 N . . . or 1,700 lbs!
Not even the winner of the World's Strongest Man contest has muscles capable of exerting a force of almost a ton. Think about it this way: To accomplish this stunt, Bourne must not only be capable of jumping six feet straight up, he has to be able to do it while holding onto a 200-pound motorcycle. Now imagine how strong Vin Diesel had to be in XXX to leap at least five times as high. This prompts the question: Why all the death-defying? With hops like that, Jason Bourne should consider a more easygoing (and lucrative) career in the NBA.—Adam Weiner