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ket accelerates by burning its onboard fuel, so its mass decreases wit ust gases are ejected with constant velocity ve (relative to the rocket v(t) = -gt – ve In(m-t) e g is the acceleration due to gravity and t is not too large. If g = 9.8 er to the nearest whole meter.)

ket accelerates by burning its onboard fuel, so its mass decreases wit ust gases are ejected with constant velocity ve (relative to the rocket v(t) = -gt – ve In(m-t) e g is the acceleration due to gravity and t is not too large. If g = 9.8 er to the nearest whole meter.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation v(t) = -gt -Ve where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s?, m = 32,000 kg, r = 130 kg/s, and ve = 3,300 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.) X m Need Help? Read It
Transcribed Image Text:A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation v(t) = -gt -Ve where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s?, m = 32,000 kg, r = 130 kg/s, and ve = 3,300 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.) X m Need Help? Read It
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