May/June 2026 Paper 43

At a particular instant, the power of the lorry's engine is $80\mathrm{kW}$ and the resistance forces on the lorry and trailer are $2400\mathrm{N}$ and $400\mathrm{N}$ respectively. At this instant, the speed of the lorry is $25m/s$. Find the tension in the tow-bar.

The lorry and trailer now descend a straight hill inclined at an angle of $5^{\circ }$ to the horizontal. As the lorry and trailer descend from a point $A$ to a point $B$ on the hill, the speed of the lorry increases from $27m/s$ to $30m/s$. The lorry's engine is no longer working at $80\mathrm{kW}$ and instead the work done by the driving force of the lorry as it travels from $A$ to $B$ is $55\mathrm{kJ}$. The resistance forces on the lorry and trailer are now $2500\mathrm{N}$ and $500\mathrm{N}$ respectively. Find the distance $AB$.