Solving for Planet Islander's Radius from a Projectile Launch

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Homework Help Overview

The problem involves determining the radius of Planet Islander based on the launch of a projectile from its surface at a specific speed related to the escape velocity. The context is rooted in gravitational physics and energy conservation principles.

Discussion Character

  • Exploratory, Conceptual clarification, Energy conservation

Approaches and Questions Raised

  • The original poster attempts to relate the escape speed to the height reached by the projectile, questioning the correct relationship between radius and height. Some participants raise questions about the conservation of energy in the context of the problem.

Discussion Status

Participants are exploring the relationship between kinetic and potential energy, with some guidance provided regarding the conservation of mechanical energy in the absence of atmospheric effects. There is an ongoing examination of the assumptions and equations necessary to approach the problem.

Contextual Notes

There is a mention of potential confusion regarding the application of escape speed and the role of height in the calculations. The discussion reflects uncertainty about the correct equations to use and the implications of energy conservation.

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Homework Statement


a projectile of mass m is launched vertically from the surface of Planet Islander at a speed that is one-third the escape speed from the surface. If the projectile reaches a maximum height that is a distance h from the surface of the planet, what is the radius of planet islander?


Homework Equations



Escape Speed = square root of G*mass/radius^2


The Attempt at a Solution



Is this the correct equation:

1/3 (G*mass/r + h) = G*mass/r

so the radius is equal to 9h? or is it 3h? or h/9?

I am confused as what to what equations to equate? and where the height comes in?

Please help!
 
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Your formula for the escape speed and none of the solutions you suggest are correct. You need that, and a consideration of the potential and kinetic energies involved at two interesting points of the projectiles flight in order to solve this problem.
 
is energy conserved in this problem? so we can equate energy at the peak and energy just before it is launched?
 
Yes, mechanical energy is conserved if you make the assumption that there are no atmosphere.
 

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