A truck of weight $$\(9000 \mathrm{~N}\)$$ is travelling up a hill on a straight road that is inclined at an angle $$\(\theta\)$$ to the horizontal, where $$\(\sin \theta=\frac{1}{15}\)$$ When the truck travels up the hill with the engine working at $$\(3 P\)$$ watts, the truck is moving at a constant speed of $$\(12 \mathrm{~m} \mathrm{~s}^{-1}\)$$ Later on, the truck travels down the hill along the same road, with the engine working at $$\(P\)$$ watts. At the instant when the speed of the truck is $$\(12 \mathrm{~m} \mathrm{~s}^{-1}\)$$, the acceleration of the truck is $$\(\frac{g}{20}\)$$ The resistance to motion of the truck from non-gravitational forces is a constant force of magnitude $$\(R\)$$ newtons in all circumstances. Find (i) the value of $$\(P\)$$, (ii) the value of $$\(R\)$$. (9)

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