Surely you've seen this commercial. "I've got all the time in the world." I can't get that song out of my head.

But clearly there are some physics in this commercial. Let's do an analysis.

How Long Can You Fall? ———————-

Here is a quick synopsis of the video. The Green Goblin's son (Harry Osborn) is partying it up as only a super villain's son can do—rooftop style. You can see the girls hanging around him, but maybe they didn't show the drinks and other stuff. Well, one thing leads to another and Harry is out on a ledge to save this girl's awesome scarf. Woops. He falls. Don't worry, Harry has the new and awesome Motorola Droid Turbo. This phone is so fast, he has all the time in the world. He uses the map to locate an awning (which would obviously have a dumpster underneath it) and then uses his special "physics app" to calculate a change to his trajectory to land on that awning.

That physics app is super awesome. It gives you both your falling speed as well as your location (I think). It's all so simple. Well, simple for the son of the Green Goblin with the Droid Turbo.

If I know the height of the fall, I can find out how long it would take to fall. If I only knew how tall that building he fell from was. If only. Well, I have the building. Thanks to my ninja-like google-Fu, I found the exact some location in Google Maps. Boom. Here is a comparison between Google Maps and the image on Harry's phone as he falls.

Images from Droid Turbo commercial and Google Maps

I'm not sure which of these buildings he fell from. It's either the Equitable Life Building (164 meters tall) or the American Surety Building (103 meters tall). Let me just calculate the falling time for both of these buildings.

Here is your standard kinematics problem from physics. A young man falls from a height of 103 meters. How long does it take him to hit the ground?

Answer: If the man falls with a constant acceleration, we can use the following kinematic equation:

Let's say the starting y-position is h and the final position is 0. Since he falls from rest, his initial y-velocity will be zero. This means we have a simpler equation.

Now I just need to put in the value for h and g = 9.8 N/kg. This gives a falling time of either 4.58 seconds or 5.79 seconds. But wait! What about air resistance? Wouldn't that make him fall a little slower and take a little bit longer? Yes, of course. However, for the 103 meter fall the fall time with air resistance is only 0.272 seconds longer. For the 164 meter fall, air resistance would increase the fall time by 0.552 seconds. Not too big of a difference.

How did I find those time differences? I promise I will show you that in a future blog post.

Is this "All the Time" in the World? Not really. Is it enough time to use your phone? No. Just look at all the stuff Harry Osborn does as he falls: pulls his phone out of his pocket, zooms in on map (which it seems like the app was already open), uses the super awesome Physics App (after opening it), sends a text message, and finally translates something. I tried doing all of these motions on my phone assuming the phone would respond fast enough. It took at least 8 seconds.

Could You Change Your Falling Trajectory? —————————————–

Let me go ahead and say that I think this "Physics App" is fake. But could you significantly alter your falling trajectory by pushing on part of the building?

Of course, I will need to start with some assumptions.

Harry can push with a force of 200 Newtons with his one arm.

The gargoyle structure is encountered after falling 25 meters.

Harry can interact with the gargoyle over a falling distance of 0.75 meters.

Ok, so Harry is going to push on this gargoyle. The first thing I need is time of the interaction (so I can use the momentum principle). Let me just use his average vertical speed and the 0.75 meters to get an approximate interaction time. If he fell 25 meters, he would be moving 22 m/s. After 0.75 meters, he will still mostly be going 22 m/s (approximately). This would give an interaction time of 0.034 seconds.

Here is where the momentum principle comes into play. The momentum principle says that the net force on an object will be equal to its rate of change of momentum. If I assume Harry only pushes in the horizontal direction, this will only change his horizontal momentum (which was zero before the interaction). Using a mass of 65 kg (just a guess), this 200 Newton push for 0.034 seconds would produce a final x-momentum of 6.8 N*s and a horizontal velocity of 0.1 m/s. That's pathetic. I would expect more from the son of a super villain.

Ok, fine. He pushed off and still will change his falling trajectory. Let's even say that I was wrong and that he could push twice as hard as I estimated giving him a horizontal speed of 0.2 m/s. How far would he divert his fall? This again is a pretty simple introductory physics problem. I'm not going into all the details (but you could look at Chapter 7 in my ebook - Just Enough Physics). Oh, sorry that I keep linking to my ebook - but I wrote that for all of you out that there want to look at the basic physics in just a tiny bit more detail. It's not a prefect book, but it doesn't suck either.

The cool thing about projectile motion is that the horizontal and vertical motions are independent. This means that I can use the constant acceleration motion in the vertical direction to find the falling time. I can then use this time in the x-direction to find the horizontal displacement. Here's what that looks like.

I can use a y 0 value of 139 meters (started from the 164 m building) and the v y0 as -22 m/s. However, even putting the final y at zero meters, I still need to use the quadratic equation to solve for the time. It's not too hard, but I will tell you that it takes 3.53 seconds for the rest of the fall. This means that Harry's horizontal displacement will be 0.706 meters. Yes. He will never make it to that dumpster. It's just not going to happen. Maybe Spider-Man will swing by and save him.

Landing in a Dumpster ———————

One last part to look at - the landing. Even though Harry couldn't make it to the awning with the dumpster underneath it, let's just pretend like he did. Could he survive? Wait. Let me change that question. Clearly Harry will survive - he's a main character in Spider-Man. Could a normal human survive this fall into an awning and then a dumpster?

You know what comes next, right? Estimations.

I am going to to with the shorter building height of 103 meters. If a human couldn't survive this, a human probably wouldn't survive from the higher building.

I need to estimate the distance over which the awning stretches. Let's say it stretches 0.5 meters before breaking.

Now I need to estimate the depth of stuff in the dumpster (hopefully soft stuff). Looking at the video, I think 1.0 meters is a fair estimate.

How fast was this human moving before hitting the awning? Using kinematic equations again, I will use an impact speed of 44 m/s (ignoring air resistance). Actually, I just checked. With air resistance he would be moving at about 38 m/s.

Last assumption. I will say that the human stops over a total distance of 1.5 meters and I will just look at the average acceleration. Really, you need to look at the maximum acceleration - but this will be a good place to start.

Oh wait. I will also assume that the gravitational force is small compared to the "stopping" force.

In order to estimate the falling person's acceleration, I will use the work energy principle. This says that the work done on the human will be equal to the change in kinetic energy. I can write this as:

I can use this to solve for the force and from that get the acceleration (assuming only a force from the awning and dumpster combined).

Using my starting speed of 38 m/s and a stopping distance of 1.5 m, I get an acceleration of 481 m/s2 or 49 g's. Is this too high of an acceleration? I think so. This site says that maximum g-force for a human impact is 100 g's. Yes, 49 g's is lower but that is an average. Ok, let me say this. It's possible to survive that fall, but I wouldn't recommend it. Either way, I doubt you would be sitting in a Chinese restaurant charging your phone after that kind of a fall.

Conclusion ———-

In the end, I think this commercial is fake. Pretty sure it's fake.