Deriving the range formula for projectile motion

[Yorganda]

I need to find a derivation of the range formula for a projectile in the absence of air.

i know that the range formula is Range=Vhxt
i know that Vh=vcostheta

but in having trouble understanding how V=Vo+at can be re-arranged to = 2Vsintheta/g=t where a=g=9.8m/s/s (gravity)

i know V=Vo+at can be arranged to equal V-Vo/g=t
but this is where i get stuck, i don't know how to get to V-Vo=2Vsintheta

i know that vsintheta = vertical velocity

If anyone can help it would be appreciated heaps

 

[cellophane]

Because of the symmetry of the parabola, the ball will hit the ground with a vertical velocity of -Vo*sin(theta). So the net change in velocity is 2*Vo*sin(theta) which takes t=2*Vo*sin(theta)/g
That's a pretty hand-wavy explanation though.