4 A golfer hits a ball from a point \(O\) on horizontal ground with a velocity of \(35 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(\theta\) above the horizontal. The horizontal range of the ball is \(R\) metres and the time of flight is \(t\) seconds.
- Express \(t\) in terms of \(\theta\), and hence show that \(R = 125 \sin 2 \theta\).
The golfer hits the ball so that it lands 110 m from \(O\).
- Calculate the two possible values of \(t\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6ae57fe9-3b6f-46c2-95b8-d48903ed796b-3_672_403_267_872}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
A toy is constructed by attaching a small ball of mass 0.01 kg to one end of a uniform rod of length 10 cm whose other end is attached to the centre of the plane face of a uniform solid hemisphere with radius 3 cm . The rod has mass 0.02 kg , the hemisphere has mass 0.5 kg and the rod is perpendicular to the plane face of the hemisphere (see Fig. 1).