2. A car of mass 600 kg tows a trailer of mass 200 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 N . The resistance to the motion of the trailer from non-gravitational forces is modelled as a constant force of magnitude 300 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 $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $P$.

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 N .
\item Use the work-energy principle to find the distance $X Y$.\\

VIIV SIHI NI III M I0N 00 :
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2022 Q2 [9]}}