How High Can a Projectile Go When Launched at 10 km/s?

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SUMMARY

A projectile launched from Earth's surface at a speed of 10 km/s reaches a maximum height of approximately 2.5 x 10^7 meters. The calculations involve gravitational potential energy and kinetic energy, specifically using the equations U = -GM/r and the conservation of energy principle. The correct approach requires considering the potential energy difference, factoring in the Earth's radius (r_E) in the calculations. The discrepancy in results arises from the misapplication of the gravitational potential energy formula.

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alexwaylo2008
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Gravitational potential energy. Please help!

Homework Statement


A projectile is launched from Earth's surface at a speed of 10 km/s. Find the maximum height it reaches.

Homework Equations


change in U = -change in K
U = -GM/r

The Attempt at a Solution


GMm/r = 1/2mv^2
((6.67x10^-11)(5.98x10^24))/r = 1/2 (10^4m/s)^2
r = 1.5x10^6 m
the answer is supposed to be 2.5x10^7 m ?
 
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Are you really taking a potential energy difference? I.e. GMm/(r-r_E) where r_E is the radius of the earth? Or did you post the wrong exponent? I definitely get 7 for the exponent, but I don't get 2.5*10^7.
 

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