What is the X component of the constant acceleration in m/s^2?

Question

On Sept. 8, 2004, the returning capsule of the Genesis Mission (which collected particles of the solar wind) crashed to earth in the Utah desert when its parachute failed to open. The capsule, which was 162 in diameter, hit the ground at 311 and penetrated the soil to 50% of its diameter.

Part A
What was the component of its constant acceleration in , as the capsule penetrated the earth?
Take the + direction to be downward, in the direction of the motion of the capsule.

Part B
What was the component of its constant acceleration in ’s, as the capsule penetrated the earth?
Take the + direction to be downward, in the direction of the motion of the capsule.

Part C
How long did it take the capsule to stop once it hit the ground?


If you could help, I would appreciate it. This is the only one I have left and it is driving me nuts. I can't figure it out. I am not sure if I am really getting what the question is asking. Any help would be greatly appreciated.

sorry, 162 cm is the diameter and it hit the ground at 311 km/h

Answer 1

Since the capsule penetrated to 50% of it's diameter, it penetrated to 81 in, or 2.06 m

What's missing for me is the angle at which the capsule struck the earth. When you have the angle, it's easy to solve.

From the looks of the pictures of the crash on the NASA site, the capsule hit perpendicular to the ground. X component zero.

The deceleration was 1800 m/s^2 in .048 seconds

you derive that by
v(t)=0=311/3.6 m/s - a*t

d(t)=2.06 m=
311/3.6 *tm/s -.5*a*t^2

solve for t first, then a

j

Answer 2

The capsule parachute did not open so it is free falling. If we ignore air resistance then it is accelerating at 9.8 m/s^2 until it impacts the ground. When it does that it buries itself to 1/2 it's diameter or 81 inches (at least I think that is what you mean but it really isn't clear). It hit the ground at 311 ( I will assume m/s since you don't give any units for this). Anyway, it takes the capsule 81 inches (again units?) to stop so:

v^2 = v0^2 + 2as
s = 81 inches (conver to m of course)
a = acceleration you are trying to find. this will be negative since the + direction is downward and this acceleration is opposite to that of gravity.
v = 0 since it comes to a stop
v0 = 311 m/s (or whatever the units are)

a = -v0^2/2s

Well that takes care of parts A and B since they seem to be the same. Or does this "accleration in" and "acceleration in 's" mean something that I am not aware of other than bad typing?

Time to stop is just:
v = v0 + at and v=0 since it stops
t = -v0 / a

Perhaps reposting with appropriate units should be done if exact answers are needed. Otherwise what is given here should be enough information for you to work out the correct answers assuming that the units are known.

Answer 3

There seems to be a little bit missing from the problem statement -- such as units.

The capsule was 162 in diameter -- meters? feet? miles?
Hit the ground at 311 -- is this a time 3:11 AM? Or is it a location: mile marker #311 on some road?

Are we to assume that the capsule decelerated at a constant rate?

Part A: component in ___ (which direction?)
Part B: what is different from Part A?

According the to mishap report, the capsule was about 1.5 meters in diameter, not 1.62 meters, but I'll use your number. It hit the ground at 311 kph.

The capsule's average deceleration was about 4607 m / s^2, or about 470 G's. It took about 19 milliseconds to stop.

Answer 4

Has anyone heard the term 'terminal velocity"? BTW at this point a=0.

Also thumbs up to Captain Mephisto