Find velocity required to reach a certain height given only height and gravity

[haiku11]

On the surface of the sun the acceleration due to gravity is approx 0.25km/s². A mass of gas forming a solar prominence rises from the sun's surface. If only gravity is considered, what must its initial upward velocity be, if it is to reach a height of 24000km above the surface?

I can't figure out how to do this, I have:
a(t) = 0.25 the integral would give me:
v(t) = 0.25t + C the integral of this would give me:
s(t) = 0.125t² + Ct + D

I'm assuming D would be 0 because that's where the prominence starts on the ground so the equation becomes:
24000 = 0.125t² + Ct
0 = 0.125t² + Ct - 24000

I don't know where to go from here because there are 2 variables and I can't do any substitution using the previous equations. Trying to use the quadratic formula made everything really messy when trying to rearrange it in terms of "t". I even tried doing this the physics way although this is a calculus problem and I still couldn't do it with the 5th motion equation because I would be trying to take the square root of a negative. But if I ignore the negative and take the root I get the approximately right answer of around 109km/s.

 

[LCKurtz]

On the surface of the sun the acceleration due to gravity is approx 0.25km/s². A mass of gas forming a solar prominence rises from the sun's surface. If only gravity is considered, what must its initial upward velocity be, if it is to reach a height of 24000km above the surface?

I can't figure out how to do this, I have:
a(t) = 0.25 the integral would give me:
v(t) = 0.25t + C the integral of this would give me:
s(t) = 0.125t² + Ct + D

I'm assuming D would be 0 because that's where the prominence starts on the ground so the equation becomes:
24000 = 0.125t² + Ct
0 = 0.125t² + Ct - 24000

I don't know where to go from here because there are 2 variables and I can't do any substitution using the previous equations. Trying to use the quadratic formula made everything really messy when trying to rearrange it in terms of "t". I even tried doing this the physics way although this is a calculus problem and I still couldn't do it with the 5th motion equation because I would be trying to take the square root of a negative. But if I ignore the negative and take the root I get the approximately right answer of around 109km/s.

If you are taking s positive upward, your acceleration should be towards the sun, therefore negative. Also, as another hint, what do you know about the velocity when it is at maximum height of 24000?

 

[haiku11]

Darn it I forgot the acceleration is negative in this case, this changes everything. Thanks.