96. We write the length unit light-month, the distance traveled by light in one month, as c·month in this solution. (a) The magnitude of the required acceleration is given by
b gc
h
010 . 3.0 × 108 m / s Δv = = 12 . × 102 m / s2 . a= Δt 3.0 days 86400 s / day
b
gb
g
(b) The acceleration in terms of g is
FG a IJ g = FG 12. × 10 m / s IJ g = 12 g . H g K H 9.8 m / s K 2
a=
2
2
(c) The force needed is
F = ma = (1.20 × 106 kg )(1.2 × 102 m/s 2 ) = 1.4 × 108 N. (d) The spaceship will travel a distance d = 0.1 c·month during one month. The time it takes for the spaceship to travel at constant speed for 5.0 light-months is
t =
d 5.0 c ⋅ months = = 50 months ≈ 4.2 years. 01 . c v
