Calculating Velocity for an Orbit Near Earth's Surface

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Homework Help Overview

The problem involves calculating the velocity required for a ball to achieve orbit near the Earth's surface, given a specific curvature of the Earth where the surface drops 32 feet for every 30,000 feet. The context is rooted in concepts of orbital mechanics and gravitational effects.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the conceptual nature of the problem, questioning how the curvature affects the ball's trajectory. There is uncertainty about the appropriate formulas for calculating velocity and the implications of the given drop in height.

Discussion Status

Some participants have expressed confusion regarding the instructor's provided answer and are seeking clarification on the reasoning behind it. There is an ongoing exploration of related questions, such as the time it takes for an object to fall a certain distance with zero initial vertical velocity.

Contextual Notes

Participants note a lack of explanation from the instructor regarding the answer provided, which has contributed to confusion. The discussion is framed within the constraints of a homework assignment, emphasizing the need for understanding rather than simply obtaining a solution.

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Homework Statement



"If the curvature of the Earth were such that the surface dropped 32 feet for every 30,000 feet, how fast would a ball have to be thrown to put it into a orbit near the ground?"


Homework Equations



I have no idea where to begin. Do I use a formula for velocity?

The Attempt at a Solution

 
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I think it's mainly sort of an 'concept' question. If the ball was in orbit, and the ground level dropped 32 feet after going 30000 ft, how far should the ball drop after traveling that same distance?
 
Thanks for the quick response. I was leaning toward that as well but then the instructor released the answer (21,289 ft/sec) but didn't explain how he arrived at that so now I am confused.
 
That's exactly the sort of answer we are after. But you didn't answer my question. But I'll continue anyway. Next question is how long does it take for a ball with zero initial vertical velocity to drop 32 ft?
 
Last edited:

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