4
\includegraphics[max width=\textwidth, alt={}, center]{5960a9cf-2c51-4c07-9973-c29604762df7-3_218_1335_251_367} Three particles \(A\), \(B\) and \(C\) are free to move in the same straight line on a large smooth horizontal surface. Their masses are \(1.2 \mathrm {~kg} , 1.8 \mathrm {~kg}\) and \(m \mathrm {~kg}\) respectively (see diagram). The coefficient of restitution in collisions between any two of them is \(\frac { 3 } { 4 }\). Initially, \(B\) and \(C\) are at rest and \(A\) is moving with a velocity of \(4.0 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) towards \(B\).

1. Show that immediately after the collision between \(A\) and \(B\) the speed of \(B\) is \(2.8 \mathrm {~ms} ^ { - 1 }\).
2. Find the velocity of \(A\) immediately after this collision.
   \(B\) subsequently collides with \(C\).
3. Find, in terms of \(m\), the velocity of \(B\) after its collision with \(C\).
4. Given that the direction of motion of \(B\) is reversed by the collision with \(C\), find the range of possible values of \(m\).