Question 963968: 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 below where g is the acceleration due to gravity and t is not too large.
http://www.webassign.net/cgi-perl/symimage.cgi?expr=v%28t%29%20%3D%20-gt%20-%20v_e%20ln%28%28m-rt%29%2Fm%29
If g = 9.8 m/s2, m = 40000 kg, r = 145 kg/s, and ve = 3000 m/s, find the height of the rocket one minute after liftoff in meter.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 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 below where g is the acceleration due to gravity and t is not too large.
http://www.webassign.net/cgi-perl/symimage.cgi?expr=v%28t%29%20%3D%20-gt%20-%20v_e%20ln%28%28m-rt%29%2Fm%29
If g = 9.8 m/s2, m = 40000 kg, r = 145 kg/s, and ve = 3000 m/s, find the height of the rocket one minute after liftoff in meter.
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v(t) is the 1st derivative of distance.
s(t) displacement = integral of v(t)
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I can do it tomorrow.
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