Projectile moving from Earth's surface

AI Thread Summary
A projectile launched directly away from Earth's surface can reach a radial distance based on its initial speed and kinetic energy. For part (a), if the initial speed is 0.500 times the escape speed, the distance can be calculated using gravitational principles. In part (b), with the initial kinetic energy at 0.500 of the escape energy, a similar approach applies. For part (c), the least initial mechanical energy required for escape can be expressed in terms of the projectile's mass (m), indicating that the mass is not needed for the calculation. Understanding these relationships is crucial for solving the problem effectively.
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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