- #1
Onus14
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Some imagination is required, so let me dress up the question a bit.
Imagine Spider-Man is on a rooftop, and he shoots a web to the top edge of a nearby building that's taller than the one he's on, in an attempt to swing toward it. Assume that the web is non-elastic and is completely adhered to the face of the building, and if he jumps off the rooftop he will naturally move in a perfect pendulum motion (ignore air resistance) A. His goal, however, is to move toward his target building following a path that is perfectly horizontal to the ground (ignore his reason) B. Keep in mind that he is able to produce a force that draws the web back into his hand, thus giving him the ability to pull himself upward if the end of the web is already attached to a surface.
http://img706.imageshack.us/img706/5889/physics.jpg"
So my question is, how much force will he need to produce from his web-hand in order to maintain the perfect horizontal path? I posit that the force will need to be dynamic/changing at each point of the fall, but can the amount of force necessary to maintain the horizontal path be elegantly described in an equation that accounts for all the variables (like building distance, time taken to travel, etc)? I gave up trying once I guessed that calculus would be involved...
If anyone is up for solving this, go for it; I'd be very interested in the solution and your thought process.
Good to be here,
~ Onus
Imagine Spider-Man is on a rooftop, and he shoots a web to the top edge of a nearby building that's taller than the one he's on, in an attempt to swing toward it. Assume that the web is non-elastic and is completely adhered to the face of the building, and if he jumps off the rooftop he will naturally move in a perfect pendulum motion (ignore air resistance) A. His goal, however, is to move toward his target building following a path that is perfectly horizontal to the ground (ignore his reason) B. Keep in mind that he is able to produce a force that draws the web back into his hand, thus giving him the ability to pull himself upward if the end of the web is already attached to a surface.
http://img706.imageshack.us/img706/5889/physics.jpg"
So my question is, how much force will he need to produce from his web-hand in order to maintain the perfect horizontal path? I posit that the force will need to be dynamic/changing at each point of the fall, but can the amount of force necessary to maintain the horizontal path be elegantly described in an equation that accounts for all the variables (like building distance, time taken to travel, etc)? I gave up trying once I guessed that calculus would be involved...
If anyone is up for solving this, go for it; I'd be very interested in the solution and your thought process.
Good to be here,
~ Onus
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