1 A car A of mass 1200 kg is about to tow another car B of mass 800 kg in a straight line along a horizontal road by means of a tow-rope attached between A and B. The tow-rope is modelled as being light and inextensible. Just before the tow-rope tightens, A is travelling at a speed of \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and B is at rest. Just after the tow-rope tightens, both cars have a speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Find the value of \(v\).
2. Calculate the magnitude of the impulse on A when the tow-rope tightens.