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**1. Homework Statement**

A projectile is shot straight up from the earth's surface at a speed of 1.40×10^4 km/hr.

How high does it go?

**2. Homework Equations**

[tex](1/2)m(v_0)^2-((G*M*m)/(R+y_0))=(1/2)mv^2-((G*M*m)/(R+y))[/tex]

**3. The Attempt at a Solution**

I assumed this is a gravitational energy problem instead of a flat Earth energy problem because of the speed for which it launched. Converting to m/s I get 3889 m/s. Using the equation above, the mass of the projectile cancels and is not needed. That provides the equation:

[tex](1/2)(v_0)^2-((G*M)/(R+y_0))=(1/2)v^2-((G*M)/(R+y))[/tex]

Since y_0 is 0 and assuming the max height is being asked for, v=0 m/s.

[tex](1/2)(v_0)^2-((G*M)/(R))=-((G*M)/(R+y))[/tex]

Solving for y:

[tex]x=-((4*G^2*M^2)/((R*(v_0)^2-2*(G*M)))*(v_0)^2)-R-((2*G*M)/((v_0)^2))[/tex]

The answer I get is 12,700km which is wrong. When I do this problem like an ordinary energy problem I get 770km for the height. Any help?