Altitude Temperature Pressure Okm 290K 101500Pa 10km 215K 25988Pa 20km 218K 5368 30km 230K 1168Pa These given altitudes correspond to starts and ends of atmospheric layers. Assume that the tem- perature varies linearly in each layer. The skydiver's freefall descent is quasi-steady, so that the drag force always balances the weight. The magnitude of the drag force is D= p² ACD, where v is the skydiver's speed, A = 1.0m² is the reference area, and Cp = 0.4 is the drag coefficient. Note that the density, p, varies with altitude, h. Assume acceleration due to gravity, 9 = 9.8m/s², remains constant, and that air is a perfect gas with gas constant R = 287J/kg.K. The skydiver remains in freefall until an altitude of 3km, at which point the parachute opens. a) The skydiver is at an altitude h in a layer whose starting temperature and pressure are To and Po, and whose constant temperature gradient is a. Show that the velocity is 이 v(h) = -C To Determine C and b as formulas in terms of the given variables. b) Show that within one layer, the time taken by the skydiver to fall from altitude h₂ to an altitude h₁ is 1-b Δε To Ca(1-b) 'T(h₂) To (T(h₁)\ To c) Using the given numerical values, determine the time spent in each layer and the total time of freefall.

Altitude Temperature Pressure Okm 290K 101500Pa 10km 215K 25988Pa 20km 218K 5368 30km 230K 1168Pa These given altitudes correspond to starts and ends of atmospheric layers. Assume that the tem- perature varies linearly in each layer. The skydiver's freefall descent is quasi-steady, so that the drag force always balances the weight. The magnitude of the drag force is D= p² ACD, where v is the skydiver's speed, A = 1.0m² is the reference area, and Cp = 0.4 is the drag coefficient. Note that the density, p, varies with altitude, h. Assume acceleration due to gravity, 9 = 9.8m/s², remains constant, and that air is a perfect gas with gas constant R = 287J/kg.K. The skydiver remains in freefall until an altitude of 3km, at which point the parachute opens. a) The skydiver is at an altitude h in a layer whose starting temperature and pressure are To and Po, and whose constant temperature gradient is a. Show that the velocity is 이 v(h) = -C To Determine C and b as formulas in terms of the given variables. b) Show that within one layer, the time taken by the skydiver to fall from altitude h₂ to an altitude h₁ is 1-b Δε To Ca(1-b) 'T(h₂) To (T(h₁)\ To c) Using the given numerical values, determine the time spent in each layer and the total time of freefall.

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