How can I fix my equation for finding initial velocity of a rocket?

[aquameatwad]

i was working on a differential equation to find the initial velocity of a rocket to get to height h.

so i have, which i got and its correct cause its the solution in the book, v^2 = 2g(R/(R+h))-2gR+V(0)^2

v = velocity
g = acceleration of gravity at Earth's surface
R= radius of earth
h = height
and i assume v(0) is the velocity v at height=0 so v(0)=0?

Problem is when i keep getting a negative number. so i assume I'm making an amateur mistake.

What am i doing wrong? I've tried converting etc. I am using km

 

[rude man]

i was working on a differential equation to find the initial velocity of a rocket to get to height h.

so i have, which i got and its correct cause its the solution in the book, v^2 = 2g(R/(R+h))-2gR+V(0)^2

Really? I'm concerned because the terms in your equation don't match dimensions. Specifically, 2gR/(R+h) does not match 2gR.

Make that very concerned.

 

[aquameatwad]

I'm trying to use this

y = R (the radius of the earth) +h ( the height i want to reach).

 

[rude man]

The last equation looks OK except there's a minor typo in it. The equation before that is OK, so use it to solve for v₀.

 

[aquameatwad]

whats the typo?

 

[rude man]

whats the typo?

Bottom equation, " v² = v₂ ". Equating velocity with velocity-squared is a no-no.