If we assume there is no air resistance, this means that the horizontal component of the ball's velocity won't change. Resolving horizontally we can see that the horizontal velocity = u*cos(θ). We can then use this to work out how far it travels using distance = speed*time, if we know how long the ball travels for. Resolving vertically, we can see that the ball's vertical velocity is u*sin(θ). We can use SUVAT equations to find how long the ball takes to fall to the ground, which is also how long the ball travels horizontally for. s = 0, as the ball is starting at the ground and is going to end back up there u = u*sin(θ) v = ? a = -g (the negative shows that it's downwards, as we're taking 'up' to be the positive direction) t = ? We can use s = ut + 0/5at^2 here. s = 0, so this simplifies to 0 = u*sin(θ)t - 0.5gt^2. We can rearrange this to: u*sin(θ)t = 0.5gt^2, which simplifies to t = 2usin(θ)/g. We can plug this into the speed equation to give distance = 2usin(θ)/g * ucos(θ). This gives distance = 2u^2 * sin(θ)cos(θ)/g As everything except from u is a constant on the right hand side, we can therefore say that distance is directly proportional to u^2.