Modeling the Motion of a Grappling Hook With a Rope

<p>So, what makes this problem fun and also challenging? If you just threw a grappling hook (or ball) upwards without a string, it&rsquo;s just plain projectile motion (assuming you ignore air resistance). However, with a rope the hook will have an extra interaction with the different parts of rope as it gets pulled off the ground.</p> <h1>Differential Equation from the Momentum Principle</h1> <p>Let&rsquo;s start off with the simplest case &mdash; a hook that is launched straight up. Here is a diagram of the hook and rope at some point after the toss.</p> <p><a href="https://rjallain.medium.com/modeling-the-motion-of-a-grappling-hook-with-a-rope-90569e47f901"><strong>Read More</strong></a></p>