\begin{enumerate} \item Two objects, \(A\) of mass 18 kg and \(B\) of mass 7 kg , are moving in the same straight line on a smooth horizontal surface. Initially, they are moving with the same speed of \(4 \mathrm {~ms} ^ { - 1 }\) and in the same direction. Object \(B\) collides with a vertical wall which is perpendicular to its direction of motion and rebounds with a speed of \(3 \mathrm {~ms} ^ { - 1 }\). Subsequently, the two objects \(A\) and \(B\) collide directly. The coefficient of restitution between the two objects is \(\frac { 5 } { 7 }\).

1. Find the coefficient of restitution between \(B\) and the wall.
2. Determine the speed of \(A\) and the speed of \(B\) immediately after the two objects collide.
3. Calculate the impulse exerted by \(A\) on \(B\) due to the collision and clearly state its units.
4. Find the loss in energy due to the collision between \(A\) and \(B\).
5. State the direction of motion of \(A\) relative to the wall after the collision with \(B\). \item A car of mass 750 kg is moving on a slope inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = 0 \cdot 1\). When the car's engine is working at a constant power \(P \mathrm {~W}\), the car can travel at maximum speeds of \(14 \mathrm {~ms} ^ { - 1 }\) up the slope and \(28 \mathrm {~ms} ^ { - 1 }\) down the slope. In each case, the resistance to motion experienced by the car is proportional to the square of its speed. Find the value of \(P\) and determine the resistance to the motion of the car when its speed is \(10 \cdot 5 \mathrm {~ms} ^ { - 1 }\).
   [0pt] [10] \item A light elastic string of natural length 1.5 m and modulus of elasticity 490 N has one end attached to a fixed point \(A\) and the other end attached to a particle \(P\) of mass 30 kg . Initially, \(P\) is held at rest vertically below \(A\) such that the distance \(A P\) is 0.6 m . It is then allowed to fall vertically.