Toy StoryBut I do know that in the trailer for the movie, which is going to be released next summer, they show Buzz launching in his spacecraft, presumably from Earth. Since the "camera" view is far away, you can see a good bit of the rocket’s motion. This makes it a perfect case for video analysis.
But why should I get the position of Buzz's rocket as a function of time? I don't know what I expect to find, and that's what makes it so exciting. So let's get started.. The first thing I need to do is to determine the video’s scale. I'm looking for an object near the spacecraft that is some known size. That's sort of difficult since everything in the scene is a computer animation—but it won't stop me. Let's use the spacecraft as our object of known size.
Let me give a brief overview of escape velocity. Suppose you take an apple and toss it up in the air with a velocity of 10 meters per second. As that apple moves upward, it’s going to slow down. Eventually, thanks to the pull of gravity, it will stop and then start falling back toward Earth.per second. Then it will get high enough such that the gravitational force won’t be strong enough to stop it. That apple will escape.
In the case of Buzz's rocket, there are essentially three force interactions during this part of the motion. First, there's the thrust from the engines. A conventional chemical engine combusts propellants to create exhaust gasses. All forces come in pairs, so when the exhaust is ejected from the engine, it pushes the rocket in the opposite direction.
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