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

AI Thread Summary
A projectile launched from Earth's surface at 10 km/s is analyzed for its maximum height using gravitational potential energy equations. The calculation involves the relationship between gravitational potential energy and kinetic energy, leading to the equation GMm/r = 1/2mv^2. A participant questions the accuracy of the expected answer of 2.5x10^7 m, suggesting a potential error in the exponent or the method of calculating the potential energy difference. The discussion emphasizes the need to consider the radius of the Earth in the calculations. Clarification on the correct approach to solving the problem is sought.
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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