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 equationv(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 atliftoff (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 equationv(t) = -gt – ve In m - rt)mwhere 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.)

Answered: A rocket accelerates by burning its…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

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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 v_e(relative to the rocket). A model for the velocity of the rocket at time t is given by the equation

v(t) = −gt − v_e 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 v_e = 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.)

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