Cassini Space Probe

[mykg4orce1]

You decide to stowaway on the Cassini Space Probe heading for Saturn. You initiate the landing procedure 8.000km above the surface of Saturn. Starting from rest, you fall for 35.5 sseconds with the engines off (you have to find the acceleration due to gravity on Saturn). Determine the following:

a) The velocity it is travelling at the end of 35.5s. b) the acceleration the engines have to be able to produce so that it doesn't crash into the ground. c) the total time it takes to land.


Given:
V1 = 0 m/s
a = 8.96 m/s^2 (Gravity of Saturn)
t = 35.5s
d = 8.000km * 1000m/km = 8000m

Velocity traveling at the end of 35.5s (V2):

V2^2 = V1^2 + 2ad
V2^2 = 0 m/s + 2 (8.96 m/s^2) (8000m)
V2^2 = 143360 m^2/s^2
V2 = 378.63 m/s
V2 = 400 m/s

Therefore, the velocity of the Cassini Space Probe at the end of 35.5s is roughly
400 m/s.

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I think i got part a) but im in total los about part b and c. Can any one help? Thanks a lot.

[sql_lall]

For a start, the first part isn't assuming you travel 8000m
(note, u = initial velocity, v = final velocity, s = distance, t = time)
(note: positive = DOWN, negative = UP)
a)
u=0 m/s (initially at rest)
t=35.5
a=8.96

v=u+at=318 m/s (3sf)
s=(v^2-u^2)/2a = 5640

b)
now, u=318
v =0
s=8000-5640=2360

a=(v^2-u^2)/2s = -21.4 (assuming constant acceleration)
incorporate gravity (=> - 8.96)
=> need to accelerate 30.4 m/s/s UP

c) I'm sure u can do this now