Mathematics 9709/41 — October/November 2012

An object is released from rest at a height of $125\text{ m}$ above horizontal ground and falls freely under gravity, hitting a moving target $P$. The target $P$ is moving on the ground in a straight line, with constant acceleration $0.8\text{ m s}^{-2}$. At the instant the object is released $P$ passes through a point $O$ with speed $5\text{ m s}^{-1}$. Find the distance from $O$ to the point where $P$ is hit by the object.