# Equation for velocity

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 earths surface
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? ive tried converting etc. im using km

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rude man
Homework Helper
Gold Member
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. :uhh:

I'm trying to use this y = R (the radius of the earth) +h ( the height i want to reach).

rude man
Homework Helper
Gold Member
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.

whats the typo?

rude man
Homework Helper
Gold Member
whats the typo?
Bottom equation, " v2 = v2 ". Equating velocity with velocity-squared is a no-no.