1 A small ball is projected from a point \(O\) on horizontal ground at an angle of \(30 ^ { \circ }\) above the horizontal. At time \(t \mathrm {~s}\) after projection the vertically upwards displacement of the ball from \(O\) is \(\left( 14 t - k t ^ { 2 } \right) \mathrm { m }\), where \(k\) is a constant.

1. State the value of \(k\).
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2. Show that the initial speed of the ball is \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
3. Find the horizontal displacement of the ball from \(O\) when \(t = 3\).