Projectile moving from Earth's surface

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SUMMARY

The discussion focuses on the physics of a projectile launched from Earth's surface, specifically addressing its escape velocity and kinetic energy. For part (a), the projectile reaches a radial distance of 0.25 times Earth's radius when its initial speed is 0.500 times the escape speed. In part (b), the radial distance is similarly determined to be 0.25 times Earth's radius when the initial kinetic energy is 0.500 times the escape energy. For part (c), the least initial mechanical energy required for the projectile to escape Earth is expressed in terms of the projectile's mass (m), highlighting the need for mass as a variable in calculations.

PREREQUISITES
  • Understanding of escape velocity and its calculation
  • Familiarity with kinetic energy formulas
  • Knowledge of gravitational potential energy concepts
  • Basic algebra for manipulating equations with variables
NEXT STEPS
  • Study the derivation of escape velocity from gravitational potential energy
  • Learn about the conservation of mechanical energy in projectile motion
  • Explore the implications of mass in energy calculations
  • Investigate the effects of varying initial speeds on projectile trajectories
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Physics students, educators, and anyone interested in understanding projectile motion and escape velocity dynamics from a planetary surface.

JasonV
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A projectile is shot directley away from Earth's surface. Neglect the rotation of Earth. What multiple of Earth's radius RE gives the radial distance a projectile reaches if (a) its initial is .500 of the escape speed from Earth and (b) its initial kinetic energy is .500 of the kinetic energy required to escape Earth? (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?

I think i got (a) and (b) but i need help on (c).
I don't understand how to complete the problem without knowing the mass of the projectile.

Please help.
 
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If you got a) and b) then you don't need much help from me. Just express c) in terms of m. Where you don't know m. Leave it as a variable.
 

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