7 The trajectory ABCD of a small stone moving with negligible air resistance is shown in Fig. 7. AD is horizontal and BC is parallel to AD .
The stone is projected from A with speed \(40 \mathrm {~ms} ^ { - 1 }\) at \(50 ^ { \circ }\) to the horizontal.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c84a748a-a6f4-48c5-b864-fe543569bdf5-4_341_1107_484_498}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure}
- Write down an expression for the horizontal displacement from A of the stone \(t\) seconds after projection. Write down also an expression for the vertical displacement at time \(t\).
- Show that the stone takes 6.253 seconds (to three decimal places) to travel from A to D . Calculate the range of the stone.
You are given that \(X = 30\).
- Calculate the time it takes the stone to reach B . Hence determine the time for it to travel from A to C.
- Calculate the direction of the motion of the stone at \(\mathbf { C }\).
Section B (36 marks)