GATE_AE_2027_MOCK_03_Q52 GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories) NAT · 2 Marks
Flight Mechanics & Space Dynamics • Space Dynamics & Orbital Mechanics • Tsiolkovsky Rocket Equation & Multistage Rockets

A rocket with initial mass m_0 = 50000 kg and propellant mass m_p = 40000 kg has effective exhaust velocity c = 3200 m/s. What is the total ideal \Delta v (in m/s) in gravity-free space? (Take \ln 5 \approx 1.6094, round to nearest integer).

Answer Key:
5150

Step-by-Step Verified Solution

### Solution: Burnout mass m_b = m_0 - m_p = 50000 - 40000 = 10000 kg. Mass ratio R = m_0 / m_b = 50000 / 10000 = 5.0. \Delta v = c * \ln(R) = 3200 * \ln 5 = 3200 * 1.60944 = 5150.2 ≈ 5150 m/s. Correct: 5150 (range 5140 to 5160).
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