Training Aerospace Engineering Placement Test Practice — Aerospace Engineering
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Placement Test Practice — Aerospace Engineering

25 min Aerospace Engineering

Placement Test Practice — Aerospace Engineering

These problems cover orbital mechanics, aerodynamics, propulsion, and atmospheric science.

Practice Test — 25 Questions

1. Find the orbital velocity at 300 km above Earth.
2. Geostationary orbit radius is 42,164 km. Find the orbital velocity.
3. Find escape velocity from a planet with $\mu = 1.27 \times 10^{17}$ m³/s² and $R = 71{,}492$ km (Jupiter).
4. Lift on a flat plate wing: $S = 10$ m², $v = 50$ m/s, $C_L = 0.5$, sea level. Find lift.
5. An aircraft weighs 20 kN, $S = 12$ m², $C_L = 1.8$. Find stall speed at sea level.
6. $I_{sp} = 450$ s. Find $v_e$.
7. $\Delta v = 4$ km/s, $I_{sp} = 350$ s, dry mass 2{,}000 kg. Find fuel mass.
8. Find the speed of sound at $h = 7$ km (ISA).
9. Mach number at 250 m/s, 5 km altitude.
10. ISA temperature at 11 km.
11. Orbital period at $a = 10{,}000$ km.
12. A rocket: $m_0 = 50{,}000$ kg, fuel = 40{,}000 kg, $I_{sp} = 300$ s. Find $\Delta v$.
13. Drag on a sphere: $C_D = 0.47$, $d = 0.1$ m, $v = 30$ m/s, sea level. Find $D$.
14. Thrust required for level flight equals drag. If $D = 5$ kN, find the required thrust.
15. Dynamic pressure at sea level, $v = 100$ m/s.
16. If $L/D = 20$ and $W = 150$ kN in level flight, find drag and thrust required.
17. Bernoulli: pressure difference across a wing if $v_{\text{top}} = 70$ m/s, $v_{\text{bot}} = 55$ m/s at sea level.
18. Semi-major axis of an orbit with $r_p = 7{,}000$ km, $r_a = 20{,}000$ km.
19. Eccentricity of the orbit in #18: $e = (r_a - r_p)/(r_a + r_p)$.
20. Vis-viva: find velocity at apogee of the orbit in #18.
21. A two-stage rocket: stage 1 mass ratio 5 ($I_{sp} = 270$ s), stage 2 mass ratio 4 ($I_{sp} = 340$ s). Find total $\Delta v$.
22. Air density at 9 km (ISA).
23. Power required: $P = Dv$. If $D = 8$ kN, $v = 80$ m/s, find $P$.
24. Rate of climb if excess power = 500 kW, $W = 100$ kN.
25. A satellite decays from 400 km to 300 km altitude. Does its speed increase or decrease? Explain.
Show Answer Key

1. $r = 6{,}671$ km; $v = \sqrt{3.986 \times 10^{14}/6.671 \times 10^6} = 7{,}726$ m/s

2. $v = \sqrt{3.986 \times 10^{14}/4.2164 \times 10^7} = 3{,}075$ m/s

3. $v_{\text{esc}} = \sqrt{2 \times 1.27 \times 10^{17}/7.149 \times 10^7} = 59{,}600$ m/s $\approx 59.6$ km/s

4. $L = 0.5(1.225)(2500)(10)(0.5) = 7{,}656$ N $\approx 7.66$ kN

5. $v_s = \sqrt{2 \times 20{,}000/(1.225 \times 12 \times 1.8)} = \sqrt{1{,}509} = 38.8$ m/s

6. $v_e = 450 \times 9.81 = 4{,}414.5$ m/s

7. $v_e = 3{,}433.5$ m/s; $m_0/m_f = e^{4000/3433.5} = 3.215$; $m_0 = 6{,}430$ kg; fuel $= 4{,}430$ kg

8. $T = 242.65$ K; $a = \sqrt{1.4 \times 287 \times 242.65} = 312.3$ m/s

9. $T = 255.65$ K; $a = 320.5$ m/s; $M = 250/320.5 = 0.780$

10. $T = 288.15 - 71.5 = 216.65$ K $= -56.5°$C

11. $T = 2\pi\sqrt{(10^7)^3/3.986 \times 10^{14}} = 9{,}952$ s $\approx 2.76$ hrs

12. $m_f = 10{,}000$ kg; $\Delta v = 2{,}943 \times \ln 5 = 4{,}737$ m/s

13. $A = \pi(0.05)^2 = 7.854 \times 10^{-3}$; $D = 0.5(1.225)(900)(7.854 \times 10^{-3})(0.47) = 2.04$ N

14. $T = D = 5$ kN

15. $q = 0.5(1.225)(10{,}000) = 6{,}125$ Pa

16. $D = 150/20 = 7.5$ kN; $T = 7.5$ kN

17. $\Delta P = 0.5(1.225)(4900-3025) = 1{,}149$ Pa

18. $a = (7{,}000 + 20{,}000)/2 = 13{,}500$ km

19. $e = 13{,}000/27{,}000 = 0.481$

20. $v_a = \sqrt{3.986 \times 10^{14}(2/2 \times 10^7 - 1/1.35 \times 10^7)} = 4{,}347$ m/s

21. $\Delta v_1 = 2{,}648.7 \times \ln 5 = 4{,}264$ m/s; $\Delta v_2 = 3{,}335.4 \times \ln 4 = 4{,}624$ m/s; Total $= 8{,}888$ m/s

22. $T = 229.65$ K; $P = 0.3080 \times 101{,}325 = 31{,}208$ Pa; $\rho = 0.473$ kg/m³

23. $P = 8{,}000 \times 80 = 640$ kW

24. $RC = P_{\text{excess}}/W = 500{,}000/100{,}000 = 5$ m/s

25. Speed increases — lower orbit means smaller $r$, and $v = \sqrt{\mu/r}$, so velocity goes up as the satellite descends.

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