A-LevelMathematicsMechanics9709/42 · Oct/Nov 2019 · Q47 Marks
A lorry of mass 25 000 kg travels along a straight horizontal road. There is a constant force of 3000 N resisting the motion.
- (i)Find the power required to maintain a constant speed of 30ms⁻¹.[2]
- (ii)The lorry comes to a straight hill inclined at 2° to the horizontal. The driver switches off the engine of the lorry at the point A which is at the foot of the hill. Point B is further up the hill. The speeds of the lorry at A and B are 30 m s⁻¹ and 25 m s⁻¹ respectively. The resistance force is still 3000 N. Use an energy method to find the height of B above the level of A.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [M1] Use of P = Fv with F = resistance
- [A1] P = 90000 W = 90kW
- [B1] Correct expression for PE Allow PE = 25 000 g d sin 2
- [B1] For either correct [KE loss = 3 437 500]
- [M1] For a 4 term work-energy equation, correct dimensions
- [A1] Correct work-energy equation involving h or d
- [A1] h = 10.2 m (10.2318...)
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