5 Mr McGregor is a keen vegetable gardener. A pigeon that eats his vegetables is his great enemy.
One day he sees the pigeon sitting on a small branch of a tree. He takes a stone from the ground and throws it. The trajectory of the stone is in a vertical plane that contains the pigeon. The same vertical plane intersects the window of his house. The situation is illustrated in Fig. 5.
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\includegraphics[alt={},max width=\textwidth]{4c8c96cf-5184-46e4-9c45-a8a80d0a6ff8-4_400_1221_1078_411}
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\caption{Fig. 5}
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- The stone is thrown from point O on level ground. Its initial velocity is \(15 \mathrm {~ms} ^ { - 1 }\) in the horizontal direction and \(8 \mathrm {~ms} ^ { - 1 }\) in the vertical direction.
- The pigeon is at point P which is 4 m above the ground.
- The house is 22.5 m from O .
- The bottom of the window is 0.8 m above the ground and the window is 1.2 m high.
Show that the stone does not reach the height of the pigeon.
Determine whether the stone hits the window.