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

[alexwaylo2008]

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 ?

 

[Dick]

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.