Suppose a super cannon fires a projectile horizontally and the projectile moves

Question

Suppose a super cannon fires a projectile horizontally and the projectile moves so fast

that it circles the Earth, always keeping the same height (~6 ft) above the ground. An identical

cannon fires an identical projectile straight up from ground level. How high would that projectile

go? (ignore air resistance)?

Mearth = 5.98x1024kg

Rearth=6.37x106m

G = 6.67x10-11 Nm2/kg2

I know the answer is: Max Height = Rearth above ground level, or 2Rearth from center of earth.

This is how I got the answer:

THE QUESTION IS:

HOW DO I GET THE ANSWER WITHOUT HAVING TO PLUG ALL THOSE NUMBERS IN? (HOW DO I REDUCE THAT UGLY EQUATION?)

Explanation / Answer

We can not reduce that equation

We should use calculator and find it's value

Because all values are in exponenets with different decimal values

So, it's better to use calculator as much as possible and get the answers

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