The points $A$ and $B$ lie 120 m apart on horizontal ground. At time $t=0$ two projectiles, $P$ and $Q$, are launched from the points $A$ and $B$. Projectile $P$ is launched with speed 40 ms^-1 at an angle of $30^{\circ }$ to the horizontal. Projectile $Q$ is launched with speed $U{ms}^{-1}$ at an angle of $\theta$ to the horizontal. At time $t=3$, $P$ and $Q$ collide. Both projectiles are modelled as particles moving freely under gravity.