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C 2mo' c) [12 marks] The magnitude of the tangential velocity v() of a space capsule during re-entry into Earth's atmosphere is given by the following equation: dv GM 1 р -vº(t) ACD m, dt (R+h(t))? 2 m(t) m(t) GM where is the acceleration due to gravity as a function of the height h of the space capsule I R+h above the surface, R is the radius of Earth, G is the gravitational constant, p is the density of the atmosphere, A is the cross-sectional area of the capsule, Cp is the capsule's drag coefficient, m= mo - mt is the time-dependent mass of the capsule due to fuel being consumed at a constant rate m = = B. and c is the magnitude of the velocity of exhaust gases burning from the capsule's thrusters to bring it into the atmosphere. Use any tool at your disposal to find the velocity for the first two time-steps, using Euler's method with a time step-size of 0.1 seconds and the values for the parameters specified in Table 1. P dm dt Table 1. Parameter values. Parameter Value (units) Description Initial mass of the capsule mo 902 kg ho 150 km Initial distance from Earth on re-entry Vo 7 844 m/s Initial velocity Gravitational constant G 6.67 x 10-11 Nm2/kg? M 5.97 x 1024 kg Mass of Earth R 6 371 km Earth's radius P 0.086 kg/m2 Density of atmosphere Area of capsule exposed to drag А 2.8 m2 CD 1 Drag coefficient