3. A car of mass 1200 kg pulls a trailer of mass 400 kg along a straight horizontal road. The car and trailer are connected by a tow-rope modelled as a light inextensible rod. The engine of the car provides a constant driving force of 3200 N . The horizontal resistances of the car and the trailer are proportional to their respective masses. Given that the acceleration of the car and the trailer is \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\),
a find the resistance to motion on the trailer,
b find the tension in the tow-rope. When the car and trailer are travelling at \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) the tow-rope breaks. Assuming that the resistances to motion remain unchanged,
c find the distance the trailer travels before coming to a stop,
d state how you have used the modelling assumption that the tow-rope is inextensible.
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