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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 In (m – rt m where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s², m = 31,000 kg, r = 160 kg/s, and ve = 2,800 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.) m

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 In (m – rt m where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s², m = 31,000 kg, r = 160 kg/s, and ve = 2,800 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.) m

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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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 ln(m-rt/m)

where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s2, m = 31,000 kg, r = 160 kg/s,and ve = 2,800 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.)

answer:_______________m 

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 In m - rt) m where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s?, m = 31,000 kg, r = 160 kg/s, and ve = 2,800 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.)
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 In m - rt) m where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s?, m = 31,000 kg, r = 160 kg/s, and ve = 2,800 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.)
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