Environmental Engineering Reference
In-Depth Information
2.9 Rocket propulsion is achieved by the emission of exhaust material at high
speed. A rocket of mass
m
travelling with velocity
v
emits exhaust gases at
constant velocity
u
relative to the rocket. Show that the net external force on
the rocket
F
satisfies
m
d
v
d
t
u
d
m
d
t
F
=
−
.
Prove that a free rocket accelerating from rest attains a final velocity
m
i
m
f
v
f
=−
u
ln
,
where
m
i
and
m
f
are the initial and final masses of the rocket.
If the rocket accelerates from rest, for a time
t
, in a uniform gravitational
field
g
show that
m
i
m
f
+
v
f
=−
u
ln
g
t.
Use the above expression to explain why space rockets are designed to burn
their fuel quickly.
