On a level stretch of road, the lorry engine delivers constant power. The resistive force opposing the motion is a constant $1600\,\text{N}$. The steady speed that the lorry can keep when the engine is operating at power $P\,\text{W}$ is $30\,\text{m s}^{-1}$. Find the value of $P$.
At the moment when the lorry is moving at $16\,\text{m s}^{-1}$, the engine is producing power of $40\,\text{kW}$. Find the acceleration of the lorry at this moment.
Once the lorry has reached a speed of $20\,\text{m s}^{-1}$, it starts to climb a section of road that is inclined at an angle $\alpha^\circ$ to the horizontal. The engine now operates at a power of $120\,\text{kW}$. Its speed does not change as it moves up the hill. The constant resistance to motion is still $1600\,\text{N}$. Find the value of $\alpha$.