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

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SUMMARY

A projectile launched straight up at a speed of 10.1 km/s from the Earth's surface will rise to a maximum height determined by gravitational potential energy. The relevant equation is U = - (Gm1m2) / r, where G is the universal gravitational constant (6.673e-11 N m²/kg²), m1 is the mass of the Earth (5.980e+24 kg), and r is the radius of the Earth (6.370e+6 m). The mass of the projectile is not required for calculating the height, as the initial kinetic energy can be equated to gravitational potential energy at the peak height.

PREREQUISITES
  • Understanding of gravitational potential energy and its formula
  • Familiarity with the universal gravitational constant
  • Knowledge of basic physics concepts such as kinetic energy
  • Ability to manipulate equations involving mass, radius, and energy
NEXT STEPS
  • Study the derivation of gravitational potential energy equations
  • Learn about kinetic energy and its relationship to projectile motion
  • Explore the concept of escape velocity and its implications
  • Investigate the effects of varying launch speeds on projectile height
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding projectile motion and gravitational effects.

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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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