Synchronise projectile flight with an approaching target

(Self-reading)

A cannonball is fired from O at speed v metres per second and angle $\theta^\circ$ above the ground. At time t seconds, $x=(v\cos\theta)t$, $y=(v\sin\theta)t-5t^2$, where x and y are horizontal and vertical displacement in metres.

(i) Find its horizontal range d when it hits the ground, in terms of v and theta.

Use $v=200$ for the remaining parts. A target approaches O along the ground at 10 metres per second, initially 3000 metres away when the cannonball is fired. Neglect the target height.

(ii) Show the possible firing angles to hit it are $22.7^\circ$ and $69.5^\circ$.

(iii) Explain which angle hits it earlier.