1 An object is released from rest at a height of 125 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 \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). At the instant the object is released \(P\) passes through a point \(O\) with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the distance from \(O\) to the point where \(P\) is hit by the object.

$[125 = \frac{1}{2} 10t^2$ | M1 | For using $h = \frac{1}{2}gt^2$
$t = 5$ s | A1 |
$[s = 5 \times 5 \frac{1}{2} 0.8 \times 5^2]$ | M1 | For using $s = ut + \frac{1}{2}at^2$
Distance is 35 m | A1 | 4

1 An object is released from rest at a height of 125 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 $0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. At the instant the object is released $P$ passes through a point $O$ with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find the distance from $O$ to the point where $P$ is hit by the object.

\hfill \mbox{\textit{CAIE M1 2012 Q1 [4]}}