Two particles \(A\) and \(B\), of mass 2 kg and 3 kg respectively, are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly. Immediately before the collision the speed of \(A\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The magnitude of the impulse exerted on \(B\) by \(A\) is 14 N s . Find
- the speed of \(A\) immediately after the collision,
- the speed of \(B\) immediately after the collision.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{278c8424-38aa-48c2-bc82-af4be9234f71-03_359_1298_219_413}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A particle of weight 8 N is attached at \(C\) to the ends of two light inextensible strings \(A C\) and \(B C\). The other ends, \(A\) and \(B\), are attached to a fixed horizontal ceiling. The particle hangs at rest in equilibrium, with the strings in a vertical plane. The string \(A C\) is inclined at \(35 ^ { \circ }\) to the horizontal and the string \(B C\) is inclined at \(25 ^ { \circ }\) to the horizontal, as shown in Figure 1. Find
(i) the tension in the string \(A C\),
(ii) the tension in the string \(B C\).