Exam-Style Problem
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Nov 2021 p42 q5
3499
A railway engine of mass 75,000 kg is moving up a straight hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.01\). The engine is travelling at a constant speed of 30 m s\(^{-1}\). The engine is working at 960 kW. There is a constant force resisting the motion of the engine.
(a) Find the resistance force.
The engine comes to a section of track which is horizontal. At the start of the section the engine is travelling at 30 m s\(^{-1}\) and the power of the engine is now reduced to 900 kW. The resistance to motion is no longer constant, but in the next 60 s the work done against the resistance force is 46,500 kJ.
(b) Find the speed of the engine at the end of the 60 s.
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