Question 5 (15 Marks) a) b) The following diagram shows the forces acting on the aircraft during a take-off ground run. DRAD WEIGHT From Newton's 2nd law, the governing equation is:

(where V is the aircraft velocity and s is the ground distance) m=T-D-p(W-L), and ==V 1) Formulate numerical approximation to BOTH equations using forward difference to compute the aircraft speed V and ground roll distances. ii) A turbo-fan aircraft has the following characteristics: Mass: m = 100,000kg Coefficient of Friction: μ = 0.02 Lift: L = 38.22V² Drag: D = 2.3271² Thrust: 7 = 90,000 N Take-off Speed: V = 78 m/s Based on the numerical approximation formulated in (1), calculate the aircraft speed V vs ground roll distances, using dt = 1 (complete the following table) Time (s) aircraft speed V (m/s) Ground Roll Distance s(m) 1 2 3 ii) Analyse the accuracy and efficient of the numerical formulation used, by commenting the effect of dr on the accuracy of the result and efficiency of the algorithm. Use your own word explain the difference between "Total Error" and "Approximation Error", and their usage