9 A pebble is thrown horizontally at \(14 \mathrm {~ms} ^ { - 1 }\) from a window which is 5 m above horizontal ground. The pebble goes over a fence 2 m high \(d \mathrm {~m}\) away from the window as shown in Fig. 9. The origin is on the ground directly below the window with the \(x\)-axis horizontal in the direction in which the pebble is thrown and the \(y\)-axis vertically upwards.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{904025c9-6d68-4344-bd41-8c0fccfcf92f-06_538_1082_452_488}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\end{figure}
- Find the time the pebble takes to reach the ground.
- Find the cartesian equation of the trajectory of the pebble.
- Find the range of possible values for \(d\).