7 At a school fair, there is a competition in which people try to kick a football so that it lands in a large rectangular box. The height of the top of the box is 1 metre and its width is 3 metres. One student kicks a football so that it initially moves at \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(50 ^ { \circ }\) above the horizontal. It hits the top front edge of the box, as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{5dd17095-18a6-470b-a24a-4456c8e3ed31-16_465_1342_625_351} Model the football as a particle that is not subject to any resistance forces as it moves.

1. Find the time taken for the football to move from the point where it was kicked to the box.
2. Find the horizontal distance from the point where the football is kicked to the front of the box.
3. If the same student kicks the football at the same angle from the same initial position, what is the speed at which the student should kick the football if it is to hit the top back edge of the box?
4. Explain the significance of modelling the football as a particle in this context.
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   \includegraphics[max width=\textwidth, alt={}]{5dd17095-18a6-470b-a24a-4456c8e3ed31-23_2488_1709_219_153}
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