Projectile Motion comparing height and initial velocity

AI Thread Summary
Two projectiles are launched at the same angle, with one reaching a maximum height twice that of the other. The initial speeds of the projectiles are in a ratio of 4:1, as derived from the relationship between maximum height and initial velocity. The formula y = yo + voy t - 0.5gt^2 can be simplified to relate maximum height directly to initial velocity, eliminating the need for time. The correct ratio of initial velocities is confirmed to be the square root of 2. Understanding these relationships is crucial for solving projectile motion problems effectively.
DarkBlitz
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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
 
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DarkBlitz said:
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.
 
I got an answer or root(2), is this correct?
 
DarkBlitz said:
I got an answer or root(2), is this correct?
Yes.
 
Thank you very much!
 

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