3. A small van of mass 1500 kg is used to tow a car of mass 750 kg by means of a rope of length 9 m joined to both vehicles. The van sets off with the rope slack and reaches a speed of \(2 \mathrm {~ms} ^ { - 1 }\) just before the rope becomes taut and jerks the car into motion. Immediately after the rope becomes taut, the van and car travel with common speed \(V \mathrm {~ms} ^ { - 1 }\).

1. Show that \(V = \frac { 4 } { 3 }\).
2. Calculate the magnitude of the impulse on the car when the rope tightens. The van and car eventually reach a steady speed of \(18 \mathrm {~ms} ^ { - 1 }\) with the rope taut when a child runs out into the road, 30 m in front of the van. The van driver brakes sharply and decelerates uniformly to rest in a distance of 27 m . It takes the driver of the car 1 second to react to the van starting to brake. He then brakes and the car decelerates uniformly at \(f \mathrm {~m} \mathrm {~s} ^ { - 2 }\), coming to rest before colliding with the van.
3. Find the set of possible values of \(f\).
   (5 marks)