A car of mass $$\(600 \mathrm{~kg}\)$$ tows a trailer of mass $$\(200 \mathrm{~kg}\)$$ up a hill along a straight road that is inclined at angle $$\(\theta\)$$ to the horizontal, where $$\(\sin \theta=\frac{1}{20}\)$$. The trailer is attached to the car by a light inextensible towbar. The resistance to the motion of the car from non-gravitational forces is modelled as a constant force of magnitude $$\(150 \mathrm{~N}\)$$. The resistance to the motion of the trailer from non-gravitational forces is modelled as a constant force of magnitude $$\(300 \mathrm{~N}\)$$. When the engine of the car is working at a constant rate of $$\(P \mathrm{~kW}\)$$ the car and the trailer have a constant speed of $$\(15 \mathrm{~m} \mathrm{~s}^{-1}\)$$ (a) Find the value of $$\(P\)$$. (5) Later, at the instant when the car and the trailer are travelling up the hill with a speed of $$\(20 \mathrm{~m} \mathrm{~s}^{-1}\)$$, the towbar breaks. When the towbar breaks the trailer is at the point $$\(X\)$$. The trailer continues to travel up the hill before coming to instantaneous rest at the point $$\(Y\)$$. The resistance to the motion of the trailer from non-gravitational forces is again modelled as a constant force of magnitude $$\(300 \mathrm{~N}\)$$. (b) Use the work-energy principle to find the distance $$\(X Y\)$$. (4)

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