Download A lunar landing craft needs to hover just above the

A lunar landing craft needs to hover just above the surface of the moon, which has a
gravitational acceleration of (1/6) g. The exhaust velocity is 2000m/s but fuel amounting
to only 20% of the total mass can be used.
How long can the landing craft hover?
Solution
Let t denote the time the landing craft can hover. Then , to find t, we use the formula
t
u
g moon
log
m0
, where
m
u is the exhaust velocity which here is 2000m/s
g moon = (1/ 6) g  (1/ 6) *9.8m / s 2
m0 is the actual mass(initial mass)
m is the final mass in presence of the external force
here since 20% of the total mass is used by fuel, the mass loss is 20%m0. hence
m  m0  0.2m0  0.8m0
4
m  m0
5
Hence t 
t
2000
m
log 0
4
(1/ 6) *9.8
m0
5
2000
5
log
(1/ 6) *9.8
4
t = 273.237s
Hence landing craft can hover 273.237 seconds.