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14.3: Spider-Man

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    In this example we’ll develop a model of Spider-Man swinging from a springy cable of webbing attached to the top of the Empire State Building. Initially, Spider-Man is at the top of a nearby building, as shown in Figure 14.1.

    14.1.jpg Figure 14.1: Diagram of the initial state for the Spider-Man example

    The origin, O, is at the base of the Empire State Building. The vector H represents the position where the webbing is attached to the building, relative to O. The vector P is the position of Spider-Man relative to O. And L is the vector from the attachment point to Spider-Man.

    By following the arrows from O, along H, and along L, we can see that

    H + L = P

    So we can compute L like this:

    L = P - H
    Exercise 14.3

    As an exercise, simulate this system and estimate the parameters that maximize the distance Spider-Man swings.

    1. Implement a model of this scenario to predict Spider-Man’s trajectory.
    2. Choose the right time for Spider-Man to let go of the webbing in order to maximize the distance he travels before landing.
    3. Choose the best angle for Spider-Man to jump off the building, and the best time to let go of the webbing, to maximize range.

    Use the following parameters:

    • According to the Spider-Man Wiki (https://greenteapress.com/matlab/spider), Spider-Man weighs 76kg.
    • Assume his terminal velocity is 60 m/s.
    • The length of the web is 100 m.
    • The initial angle of the web is 45° to the left of straight down.
    • The spring constant of the web is 40 N/m when the cord is stretched and 0 N/m when it’s compressed.

    This page titled 14.3: Spider-Man was last modified on Thu, 17 Nov 2022 18:20:23 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Allen B. Downey (Green Tea Press) via source content that was edited to the style and standards of the LibreTexts platform.