- \hspace{0pt} [In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, \(\mathbf { i }\) being horizontal and j being vertically upwards.]
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b6e93edf-1b9f-4ea9-bb41-f46f380bc623-22_398_1438_420_267}
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\caption{Figure 3}
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A golf ball is hit from a point \(O\) on horizontal ground and is modelled as a particle moving freely under gravity. The initial velocity of the ball is \(( 2 u \mathbf { i } + u \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) The ball first hits the horizontal ground at a point which is 80 m from \(O\), as shown in Figure 3.
Use the model to
- show that \(u = 14\)
- find the total time, while the ball is in the air, for which the speed of the ball is greater than \(7 \sqrt { 17 } \mathrm {~m} \mathrm {~s} ^ { - 1 }\)