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94 Chapt. 9 Momentum
c) Write down the equation of motion again and solve for acceleration
a
as a function of time.
Assume that mass change rate is a constant (which implies that thrust is constant) and
solve for velocity as a function of time.
HINT:
Write mass as
m
(
t
) =
m
0
+ (
dm/dt
)
t
,
where
m
0
is initial mass.
d) Assuming the gravity is negligible, use the result of part (c) to solve for the time
t
it take to
reach escape velocity 11
.
2 km
/
s? Use the mass rate change found in part (b). By evaluating
gt
assess if gravity is in fact negligible? How much mass has the rocket lost in achieving
escape velocity?
009 qfull 00800 3 5 0 tough thinking: multistage rocket
Extra keywords:
Fr359912, but highly modi±ed
7. Consider a fullyfueled, multistage rocket at rest in gravityfree space. There are
I
stages plus
the payload which we will call stage
I
+ 1, but the payload has no fuel. The mass of stage
i
is
n
i
m
, where
m
is the mass of the payload and
n
i
is a dimensionless mass ratio:
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 Fall '06
 Buchler
 Physics, Acceleration, Mass, Momentum

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