# Height after 1 minute given an equation

• Oct 27th 2008, 04:42 PM
sfgiants13
Height after 1 minute given an equation
Suppose the initial mass of the rocket at liftoff is m including fuel, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity vsube (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation

v(t)=-gt-vsube ln[(m-rt)/m] where g is the acceeration due to gravity and t is not too large. If g is 9.8 m/s^2, m=30000 kg, r=160 kg/s, and vsube=3000 m/s, find the height of the rocet one minute after liftoff.

So I know I need to integrate from 0 to 1 (I think), but how in the world do I do that with this equation.
• Oct 27th 2008, 07:20 PM
skeeter
Quote:

Originally Posted by sfgiants13
Suppose the initial mass of the rocket at liftoff is m including fuel, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity vsube (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation

v(t)=-gt-vsube ln[(m-rt)/m] where g is the acceeration due to gravity and t is not too large. If g is 9.8 m/s^2, m=30000 kg, r=160 kg/s, and vsube=3000 m/s, find the height of the rocet one minute after liftoff.

So I know I need to integrate from 0 to 1 (I think), but how in the world do I do that with this equation.

don't believe this is meant to be done by hand ... get out your calculator and integrate v(t) from 0 to 60 since time for all the given units are in seconds.