5.
\begin{figure}[h]
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\caption{Figure 3}
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\end{figure}
Figure 3 represents the scene of a road accident. A car of mass 600 kg collided at the point \(X\) with a stationary van of mass 800 kg . After the collision the van came to rest at the point \(A\) having travelled a horizontal distance of 45 m , and the car came to rest at the point \(B\) having travelled a horizontal distance of 21 m . The angle \(A X B\) is \(90 ^ { \circ }\).
The accident investigators are trying to establish the speed of the car before the collision and they model both vehicles as small spheres.
- Find the coefficient of restitution between the car and the van.
(5)
The investigators assume that after the collision, and until the vehicles came to rest, the van was subject to a constant horizontal force of 500 N acting along \(A X\) and the car to a constant horizontal force of 300 N along \(B X\). - Find the speed of the car immediately before the collision.
(9)