Ratio of initial speeds for projectiles with different max heights

[DarkBlitz]

Hey,
I came across this question in my textbook, and there isn't an answer for it in the back, so I would just like to check if I have my head around it.

The question is:
2 projectiles are launched at the same angle. Projectile 1 reaches a max height of twice that of the projectile 2. What is the ration of the initial speeds?

I said that they where in the ratio 4:1, as one of the formulas is: y=yo +voyt -0.5gt^2
and because the height is doubled, the time taken must also be doubled?
am I correct in saying this?

Thanks

 

[Doc Al]

I said that they where in the ratio 4:1, as one of the formulas is: y=yo +voyt -0.5gt^2
and because the height is doubled, the time taken must also be doubled?
am I correct in saying this?

No.

Come up with a formula that relates max height with initial velocity without the need for the time.

 

[DarkBlitz]

I got an answer or root(2), is this correct?

 

[Doc Al]

I got an answer or root(2), is this correct?

Yes.

 

[DarkBlitz]

Thank you very much!