The only way I can deal with my excitement over the Spider-Man: Homecoming trailer is to do what I do best---apply some physics to the cool stuff I see in it.
In this case, I want to analyze Spider-Man's epic jump onto the Staten Island Ferry as it pulls away from the dock. You can see it about one minute into the trailer. Why does he make this jump? Who knows. But video analysis lets me plot his position as a function of time. I love video analysis, and usually start by finding the scale of any objects in the scene. I'm in luck here, because the Staten Island Ferry is a real thing. After studying a few images, I feel confident saying the webbed wonder leaps onto an Austen class ferry with a length of 63 meters. Boom. There's my scale.
From there, it's a simple matter of using software like Tracker Video Analysis to determine Spidey's position. Here is the horizontal motion as a function of time:
Although this plot looks boring, it's actually very good. It shows that Spider-Man's horizontal position (x-position) changes at a constant rate. The slope (7.65 m/s) represents his horizontal velocity in the air, and is exactly what you expect of a moving object with only gravitational force acting on it. Since gravity pulls down, not sideways, there is no horizontal forces and therefore no horizontal acceleration.
Now for the vertical motion.
This data look mostly parabolic---as you'd expect. With only the gravitational force in the vertical direction, the position vs. time plot should be a parabola. Using a quadratic equation, I get a vertical acceleration of 7.8 m/s2. This isn't too far off from the expected acceleration of 9.8 m/s2 (or as many call it, g). But why the discrepancy? Perhaps my scale is off. It could be that the director used just a bit of slow motion for added effect. Or maybe, just maybe, that's not a real person making the leap, but a CGI effect.
But wait! There's more. The trailer also shows Spider-Man landing on the ferry. The trailer provides just a few frames, but I can make some rough estimates. Here is Spider-Man's vertical position during the landing:
Although, strictly speaking, Spidey continues accelerating while falling, I used three position points to determine his landing speed. Based on the slope of this line, he hits the ground at about 11 m/s. That's not a terrible value. Assuming a constant vertical acceleration of 9.8 m/s2, the following kinematic equation reveals the final velocity:
Using an initial velocity of zero m/s results in a falling height of 6 meters. That's not crazy.
Here are some physics homework questions for you, since Peter Parker studies physics:
- As best I can tell, Spidey leaps from Whitehall Terminal onto the ferry. Find the terminal on Google Maps or something like that, estimate the height of the ledge he jump from, and calculate his landing speed.
- Then use that height to calculate Spidey's free fall time. Compare it to his falling time in the trailer.
- Using my last plot of vertical position vs. time, calculate Spider-Man's acceleration during his landing. Could a normal human survive this?
- The ferry is moving at a speed of about 0.44 m/s (I measured this from the video). If Spider-Man started 6 meters above the ferry deck, how fast would he have to run and jump (horizontally) so that he caught a ferry that started from point with a horizontal distance of 14 meters from where Spider-Man started? Yes, this one is tougher. But no one said analyzing movie trailers is easy.
https://www.youtube.com/watch?v=DiTECkLZ8HM
