- \hspace{0pt} [In this question the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertically upwards.]
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ad09e19e-c4f3-4b93-9e9a-4987def62f26-11_375_1008_354_475}
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\caption{Figure 3}
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The point \(O\) is a fixed point on a horizontal plane. A ball is projected from \(O\) with velocity \(( 3 \mathbf { i } + v \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 } , v > 3\). The ball moves freely under gravity and passes through the point A before reaching its maximum height above the horizontal plane, as shown in Figure 3.
The ball passes through \(A\) at time \(\frac { 15 } { 49 } \mathrm {~s}\) after projection. The initial kinetic energy of the ball is \(E\) joules. When the ball is at \(A\) it has kinetic energy \(\frac { 1 } { 2 } E\) joules.
- Find the value of \(v\).
At another point \(B\) on the path of the ball the kinetic energy is also \(\frac { 1 } { 2 } E\) joules. The ball passes through \(B\) at time \(T\) seconds after projection.
- Find the value of \(T\).