The range is the horizontal distance traveled before the projectile hits the ground.
The distance covered in the x-direction is simply:
x = vox t
To find the range, use t as the time of flight, which we just calculated to be:
t = 2 vo sin(θ) / g
Plugging in vox = vo cos(θ) gives:
x = 2 vo2 sin(θ) cos(θ) / g
Using the trig. identity 2 sin(θ) cos(θ) = sin(2θ) this can be written as:
x = vo2 sin(2θ) / g
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