A-LevelMathematicsMechanics9709/41 · May/June 2019 · Q37 Marks
A lorry has mass 12000 kg.
- (i)The lorry moves at a constant speed of 5 m s⁻¹ up a hill inclined at an angle of θ to the horizontal, where sin θ = 0.08. At this speed, the magnitude of the resistance to motion on the lorry is 1500 N. Show that the power of the lorry's engine is 55.5 kW.[3]
- (ii)When the speed of the lorry is v m s⁻¹ the magnitude of the resistance to motion is kv² N, where k is a constant. Show that k = 60.[1]
- (iii)The lorry now moves at a constant speed on a straight level road. Given that its engine is still working at 55.5 kW, find the lorry's speed.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] Using DF = Resistance + weight component (3 terms)
- [M1] Using P = Fv (their 2 term DF × 5)
- [A1] AG
- [B1] AG
- [B1] Using DF = resistance = 60v²
- [M1] P = Fv used and attempt to solve a 2-term cubic equation for v
- [A1] v = 9.74 ms⁻¹
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