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Category > Physics Posted 08 May 2017 My Price 7.00

Extra credit 1

Extra credit 1
(Dated: 2 April, 2017) The rocket equation determines the maximum change in velocity of a rocket that propels itself by
ejecting mass at a fixed velocity ve in the absence of external forces. You can imagine the common
picture of a rocket that accelerates by burning solid or liquid fuel and directing the combusting
fuel out one end of the rocket to propel it in the other direction. The change in velocity is given
by

vf − vi = −ve ln mf
mi 
(1) where vf is the final velocity of the rocket, vi is the initial velocity, mf is the final mass of the
rocket (plus any remaining fuel) and mi is the initial mass of the rocket and fuel.
1. [1 percentage point] Derive the maximum change in velocity in case the exhaust velocity
is proportional to remaining fuel (instead of a constant). You can think of this is as a model of
water rocket, in which the pressure of the water is proportional to the amount of water and gas in
the bottle. Note this is different from the exhaust velocity being proportional to the mass of the
rocket plus remaining fuel. Hint: it will help to present the derivation of Equation (1) in your own
words so you understand where it comes from.
Plot the maximum velocity change as a function of fuel to rocket mass ratio, (mi − mdry )/mdry
where mdry is the mass of the rocket with no fuel. Compare to the constant ve rocket equation, by
plotting the same function based on Equation (1) as well. 2. [1 percentage point] Determine the final momentum of the rocket after all fuel is expended
and the displacement at the moment the fuel is expended. Compare the ve =constant case to the
case solved in Problem 1.

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SuperTutor
(15)
Status NEW Posted 08 May 2017 05:05 AM My Price 7.00

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