- \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]{e6e37d85-f8de-490a-82a9-8a3c16e2fdd0-20_289_837_347_486}
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\caption{Figure 5}
\end{figure}
A small ball is projected with velocity \(( 6 \mathbf { i } + 12 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) from a fixed point \(A\) on horizontal ground. The ball hits the ground at the point \(B\), as shown in Figure 5. The motion of the ball is modelled as a particle moving freely under gravity.
- Find the distance \(A B\).
When the height of the ball above the ground is more than \(h\) metres, the speed of the ball is less than \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
- Find the smallest possible value of \(h\).
When the ball is at the point \(C\) on its path, the direction of motion of the ball is perpendicular to the direction of motion of the ball at the instant before it hits the ground at \(B\).
- Find, in terms of \(\mathbf { i }\) and \(\mathbf { j }\), the velocity of the ball when it is at \(C\).