7 Fig. 4 shows a particle projected over horizontal ground from a point O at ground level. The particle initially has a speed of \(32 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) to the horizontal. The particle is a horizontal distance of 44.8 m from O after 5 seconds. Air resistance should be neglected.
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\caption{Fig. 4}
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- Write down an expression, in terms of \(\alpha\) and \(t\), for the horizontal distance of the particle from O at time \(t\) seconds after it is projected.
- Show that \(\cos \alpha = 0.28\).
- Calculate the greatest height reached by the particle.