- \hspace{0pt} [In this question, the perpendicular unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane with \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertically upwards.]
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{52966963-2e62-4361-bcd5-a76322f8621e-24_679_1009_347_529}
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\caption{Figure 4}
\end{figure}
A small ball is projected with velocity \(( 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) from the fixed point \(A\).
The point \(A\) is 20 m above horizontal ground.
The ball hits the ground at the point \(B\), as shown in Figure 4.
The ball is modelled as a particle moving freely under gravity.
- By considering energy, find the speed of the ball at the instant immediately before it hits the ground.
- Find the direction of motion of the ball at the instant immediately before it hits the ground.
- Find the time taken for the ball to travel from \(A\) to \(B\).
At the instant when the direction of motion of the ball is perpendicular to ( \(3 \mathbf { i } + 2 \mathbf { j }\) ) the ball is \(h\) metres above the ground.
- Find the value of \(h\).