What is the Speed of the Package at Maximum Height?

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Homework Help Overview

The problem involves a package launched from Earth's surface at an angle of 51.0 degrees, reaching a maximum height equal to Earth's radius. Participants are tasked with determining the speed of the package at this height and the initial launch speed, while ignoring air resistance and Earth's rotation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the conservation of energy and momentum, questioning how kinetic energy relates to vertical and horizontal components of velocity. They discuss the implications of the launch angle on energy calculations and the need for multiple conservation equations.

Discussion Status

There is ongoing exploration of different approaches to the problem, with participants providing various calculations and questioning the correctness of their methods. Some guidance has been offered regarding the use of gravitational potential energy and the need to consider both kinetic and potential energy in their equations.

Contextual Notes

Participants are grappling with the implications of large changes in height on gravitational potential energy and are encouraged to reconsider their assumptions about energy conservation in this context. The discussion reflects a mix of correct and incorrect reasoning, with no clear consensus reached yet.

  • #31
It often helps to draw pictures. But yes, the angle between the radial and velocity vectors would be 39 degrees at launch. What is the angle going to be at the maximum altitude?

Think about it, sketch some pictures. It might help to bring the picture a bit closer to Earth. For example, imagine a baseball thrown from center field to home. At the top of the baseball's arc, what is the angle between the ball's velocity vector and local vertical?
 
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  • #32
Isnt it 90 degrees because at the top of the arc (or maximum altitute) there is only velocity in the horizontal direction and none in the vertical?
 
  • #33
Correct.

What's next? Can you finish this problem now?
 
  • #34
Yes that helps. I am going to rework the problem this weekend when i am studying for my test and if i run into any problems i will post here again.

Thank you for all the help.
 

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