I'm having some difficulty with a homework problem which states:(adsbygoogle = window.adsbygoogle || []).push({}); A cannonball is shot straight up out of a very powerful cannon located at the South Pole and reaches a maximum height of one Earth radius above the surface of the Earth. What was its initial speed? How long did it take to reach its max height?

The relevant equations I've gathered are:

1. Radius of Earth Re = 6.4*10^6 meters.

2. Escape Velocity Ves = (2GM/ro)^(1/2), where ro=Re.

3. v^2 = Vo^2+2GM(1/r - 1/ro). Is v the final velocity at its max height if I plug in Re for r and ro?

4. Time to reach max height [itex]\tau[/itex] = (2/GM)^(1/2)*rmax^(3/2)*[([itex]\pi[/itex]/4)-([itex]\theta[/itex]o/2)+(sin2[itex]\theta[/itex]o/4)] What would [itex]\theta[/itex]o represent in this equation? I'm assuming zero since the cannon is shot straight up.

I would like to know how I would approach the problem using these equations. Would I have to calculate escape velocity and then calculate an additional velocity exerted by the cannonball after it escapes earth and travels an additional Re? Any help would be greatly appreciated. Thanks.

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# Cannonball shot off of Earth, Escape velocity, max height

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