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My end goal is to calculate the vertical and horizontal displacement of an object that explodes in the air e.g. a firework. However, I am having difficulty deriving the initial velocity of the object. I know the approximate time is 5.0 seconds from the ground to explosion and the height is 600 ft (182.88m).

So far I have used the equations v(i) = (d / t) - [(a * t) / 2] and V(i) = a*t. Any help would be greatly appreciated.

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# Initial Velocity - Projectile Motion

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