Need help with derivation of the range formula

[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

 

[Google_Spider]

Hi,

If you take downward direction to be +ve then

$$V=vsin \theta$$

and

$$V_o=-v sin \theta$$

a=g

Put this in your equation.