How High Will a Projectile Rise if Launched at 10.1 km/s?

AI Thread Summary
A projectile launched at 10.1 km/s from the Earth's surface will rise to a specific height determined by gravitational potential energy. The universal gravitational constant, Earth's radius, and mass are essential for calculations, but the mass of the projectile is not needed for determining maximum height. The kinetic energy of the projectile at launch must equal the gravitational potential energy at its peak height. The discussion also touches on the relevance of potential energy in physics, its units, and related formulas. Understanding these concepts is crucial for solving the problem effectively.
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At the Earth's surface a projectile is launched straight up at a speed of 10.1 km/s. To what height will it rise?
Universal gravitational constant = 6.673e-11 N m^2/kg^2
Radius of the Earth = 6.370e+6 m
Mass of the Earth = 5.980e+24 kg

I know to use the equation U= - (Gm1m2)/ r
I also need to take into consideration that r is the radius of the Earth and the object is launched at the surface of the earth. However how am I suppose to solve for height when their is no mass of the projectile and what do I do with the speed of the projectile. I originally thought I should consider that U=mgy but that got me nowhere. Any help will be appreciated I'm literally teaching this to myself.
 
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what do you use potential energy for in physics? what are the units of P.E. what other formual has the same units?
 
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