projectile motion: calculating initial speed from flight time

[doubledoctordoubletrouble]

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According to the explanation for this problem, if we only know the flight time of the projectile fired vertically upward from ground level, we can calculate the initial speed using the following equation:

v = g(T/2)

I have never seen this equation before. Can someone please explain how this was derived and the concept behind it?

 

[Cawolf]

a = -g

v = v0 - gt

vz = v0z - gt

vz = 0 at the top of the flight

0 = v0z - gt

v0z = gt

So this is the velocity of an object shot upwards that takes time = t to reach the top of the flight path.

t = v0z/g for half the flight and therefore the whole flight will take twice as long t = 2v0z/g

You can then rearrange and solve for voz = gt/2.