What is the formula for determining the velocity of a rocket launched off Earth?

[gbaby370]

I am doing a problem which involved determining how fast a rocket was launched off the Earth to reach a maximum height.

I am looking for some assistance with some simple algebra.

The formula used is;

Etotal = -Gm1m2/r+0.5m2v^2

To isolate for v, would my equation be;

v=sqrt(2(Etotal+(Gm1/r))

 

[Doc Al]

The formula used is;

Etotal = -Gm1m2/r+0.5m2v^2

OK.

To isolate for v, would my equation be;

v=sqrt(2(Etotal+(Gm1/r))

Not exactly. (You missed an m2 in there.)

But instead of doing this, express the total mechanical energy at the highest point and compare it to that at the starting point. Then you can make use of energy conservation.

 

[gbaby370]

Thanks for your help!

I looked over it again and found the answer I was looking for.

 

[gbaby370]

Ok so I rearranged and got the correct answer. I was just wondering if this equation I've attached can be reduced even further?

 

[Doc Al]

I would combine those fractions using a common denominator.

 

[gbaby370]

Ok, how does this look?

 

[Doc Al]

Looks good to me. (You can even put the 2 in the numerator and erase one set of parentheses.)

 

[gbaby370]

Oh ya?

Thanks for you help.