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Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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An Ace Attorney physics problem!

Rule: Define an "undiscovered" corpse as one that has not been seen by anybody but the murderer and any accomplices. Where details of time or distance are unavailable, make a reasonable estimate.

Intro problem: What has a higher average speed - a snail, or an undiscovered corpse?

Spoiler: AA1:
1-1: Corpse not moved.
1-2: Corpse not moved.
1-3: Jack Hammer is killed. Before he is discovered, he is moved between two film studios.
1-4: Hammond's corpse is moved from the shore to Gourd Lake before discovery - not far.
1-5: Goodman's corpse is moved from the police department to the prosecutor's office; I believe a length is given for the drive, but I don't remember it. This may be a distance record!

Scene-of-the-crime shifts: 3 out of 5.


1. Please estimate the average velocity of an undiscovered corpse in AA1.

Spoiler: AA2:
2-1: Corpse not moved.
2-2: Corpse not moved.
2-3: Corpse not moved.
2-4: Corpse not moved.

Scene-of-the-crime shifts: 0 out of 4.


2. Please estimate the average velocity of an undiscovered corpse in AA2.

Spoiler: AA3:
3-1: Either corpse or power lines are moved; I forget which. Either way, not a great distance.
3-2: Corpse is hidden in safe. A few feet of movement, max.
3-3: Corpse is moved to kitchen and back to seat.
3-4: Corpse is moved to trunk, but not carried off in car.
3-5: Flying corpse-on-a-rope!

Scene-of-the-crime-shifts: 1 out of 5.


3. Please estimate the average velocity of an undiscovered corpse in AA3.

Spoiler: AA4:
4-1: Corpse not moved.
4-2: Edit: Corpse not moved.
4-3: LeTouse's body is moved onto the stage platform.
4-4: Corpse not moved.

Scene-of-the-crime shifts: 1 out of 4


4. Please estimate the average velocity of an undiscovered corpse in AA4.

Spoiler: AAI:
AAI-1: Corpse not moved.
AAI-2: Corpse packed in a suitcase and sent up an elevator shaft. Postulated crime scene changes twice.
AAI-3: Corpse moved from haunted house to garage. Fake crime scene in stadium; crime scene changes twice.
AAI-4: Corpses not significantly moved.
AAI-5: Corpse moved by water. Crime scene changes once.

Scene-of-the-crime shifts: 5.


5. Please estimate the average velocity of an undiscovered corpse in AAI.

6. If you answered the intro question in the negative, please reassess.


Last edited by FerdieLance on Sat Mar 20, 2010 5:37 am, edited 1 time in total.
Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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Idol of Polar Bears

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FerdieLance wrote:
An Ace Attorney physics problem!

Rule: Define an "undiscovered" corpse as one that has not been seen by anybody but the murderer and any accomplices. Where details of time or distance are unavailable, make a reasonable estimate.

Intro problem: What has a higher average speed - a snail, or an undiscovered corpse?


Corpses are not autonomous and, therefore, are incapable of gaining self-sustainable velocity. Snails is clearly the correct choice!
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Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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(Sp)ace Detective

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I need a life.

Assume only time spent in motion counts, and disregard corpses that don't move. Averages are all sum of distance traveled by corpses over sum of time each corpse takes. Also, time taken for people to discover the corpse isn't counted.
Spoiler: PW1
1-3: Estimate corpse moves 15 m traveling between the van and Studio Two fence/Studio One interior, van moves 80 m. Since window of opportunity was only 15 minutes and Vasquez and Manella would looks suspicious if they were late for the meeting, assume actual corpse motion takes 5 minutes (leaving 10 minutes for Vasquez to confer with Manella, stage the murder area, and get back to Studio Two after the deed is done).

v = 95/300 = 0.316 m/s
Seems a bit too low...

1-4: Corpse is moved 50-100 m to middle of lake, and drifts same distance up to edge of lake (or close enough to be found). Hammond was killed at 11:50, so assume corpse is in water 10 minutes later. It's found the next morning, but it's not stated how long it was there. Assume it takes 4 to 8 hours to reach edge of lake.

min v = 200/240 = 0.833 m/s
max v = 100/480 = 0.208 m/s

1-5: Travel time between Prosecutor's Office and Police Department is 30 minutes; 30 km is a reasonable distance estimate. Assume time and distance Gant spends moving body into Edgeworth's car is negligible.
v = 30000/1800 = 16.667 m/s

Average velocity of four possible bodies = 10.778 m/s


Spoiler: T&T
3-1 to 3-4: Since all corpses are moved by hand over short distances, assume they all travel at about the same speed. Let's just call it 0.5m/s.
Actually, since Glen Elg's body ended up right back where it started, its displacement and therefore its velocity should be technically zero.

3-5: Treated separately.


Spoiler: AJ
Can't be bothered. :yuusaku:


Spoiler: AAI
AAI-3: Distance between Haunted House entrance and garage appears to be no more than 70m based on distance between front gate and bridge over the moat thingy (assuming the pamphlet map is to scale). What a small theme park!
Assume it takes 3 minutes to move body 20m into Meekins' Badgermobile and Meekins spends 15 minutes driving around before parking the mobile in garage.
v = 90/1080 = 0.083 m/s

AAI-2 and AAI-5: Will do later maybe?


Here's the really hard one:
Spoiler: 3-5
The bridge is about 20 yards long. We'll take a short cut and do "1 yard = 1 meter".
Ignore friction and air resistance, assume cables have negligible mass and treat Misty Fey as a point mass.

Support cables are at about 45 degrees to bridge axis. The east-west distance covered by each cable is about 7 meters, so the minimum cable length is:

l = 7 x (cos 45)^-1
= 9.899 m
Round up to 11 meters, to allow the cable some slack (it needs it anyway to cope with expansion/contraction with temperature).

Assume Misty Fey and her clothes and such on her body mass 55 kg. She's going to need some help getting over to the other side, so Godot gives her a shove at the start of the swing, imparting an initial velocity of 4 m/s.

The velocity she has at the bottom of the swing, not counting that initial shove and using the mgh approximation for gravitational potential energy:

0.5mv^2 = mgh <- Conveniently for us, the mass terms cancel out.
v^2 = 19.6 x 11
v = 14.68 m/s

Adding Godot's shove gives us 18.68 m/s peak velocity.

If the corpse detaches when the cable is at 30 degrees to the horizontal, it'll be 11 sin 30 = 5.5 m below its starting point. Velocity from GPE at this point:

v^2 = 19.6 x 5.5
v = 10.383 m/s

Adding 4 m/s, that's 14.383 m/s initial velocity for the free flight.

Misty is now flying at 60 degrees to the horizontal, so her horizontal velocity for the remainder of the flight will be 14.383 cos 60 = 7.191 m/s.
Her current vertical velocity is 14.383 sin 60 = 12.456 m/s.
The peak height she can reach, with zero being her position at launch:

12.456^2 = 19.6h
h = 7.916 m

However, since she started 5.5m below the bridge level, said peak height is only 2.41 m, or 7.925 ft. Not exactly a 10-foot drop, even with all the generous assumptions we've been making. :yuusaku:

Her vertical velocity after falling 2.41m:

v^2 = 19.6 x 2.41
v = 6.873 m/s

Thus, her velocity at impact (for those of you who are only slightly math-savvy, this part is just Pythagoras's Theorem):
v = sqrt(6.873^2 + 7.191^2) = 9.947 m/s

Ain't physics grand? :scientific:

Actually, we still need to establish Misty's average velocity from Godot's position to Iris's position and maybe the velocity of the body on the snowmobile ride, but my brain hurts enough as it is without getting into calculus so I think I'll stop for now.


And there we have it. Since all the calculated velocities are much higher than a snail's velocity (something like 1mm/s), we can safely say that an undiscovered corpse does in fact move faster than a snail.
Maybe I'll redo the whole thing to include stationary corpses and discovery time if I ever get bored.
Read my fic(s)!
Friedrich Nietzsche wrote:
We have no dreams at all or interesting ones. We should learn to be awake the same way — not at all or in an interesting manner.
Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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kills at the whim of a hat

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I cannot follow this in the slightest.

But
Spoiler: 4-2
Quote:
4-2: Meraktis's body is carried a few blocks in a noodle stand.
Objection? If memory serves, he stays where he was shot.
He was shot while he was moving someone else thought to be dead and they killed him from inside the noodle stand, right?

Newfound bloggery
Please take a look. I'd appreciate any comments too!

Thanks to Berendsnor for the avatar.
Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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...Hopefully someday... xD

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Location: Suomi, Finland, Perkele!

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FerdieLance wrote:
Spoiler: AA4:
4-2: Meraktis's body is carried a few blocks in a noodle stand.

I don't get this one...I thought Meraktis was killed by Alita,
while Meraktis himself tried to carry "Alitas body" int the noodle stand.
What I've miss'd?

EDIT: ok, thanks.
"It's all becoming clear to me now....Zvarri!" :P
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Last edited by Zinle on Sat Mar 20, 2010 7:30 am, edited 1 time in total.
Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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Idol of Polar Bears

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Zinle wrote:
FerdieLance wrote:
Spoiler: AA4:
4-2: Meraktis's body is carried a few blocks in a noodle stand.

I don't get this one...I thought Meraktis was killed by Alita,
while Meraktis himself tried to carry "Alitas body" int the noodle stand.
What I've miss'd?


Meraktis tried to carry the body in his car but it wouldn't start because Trucy's panties were jammed into the exhaust pipe, so he emptied Eldoon's noodle cart and carried the body that way.

EDIT: Yeah, there's a problem with that one. Meraktis wasn't the one who was carried in the stand; it was Alita but she was just unconscious.
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Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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*imagines alita trting to carry him*
Sig.
Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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Prosecutor

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My mistake; editing to fix.

... though this does make the discrepancy in "number of corpse movement schemes" in AAI versus the other games even more marked. Seriously, AAI corpses just can't sit still.

KingRaptor: Kudos for dissecting the corpse's trajectory! This definitely gives us the peak corpse velocity in the game. An interesting problem would be to work out how, exactly, one could generate a 10-meter drop if we assume Misty's weight is accurate, but the bridge and cable dimensions are less accurate.

EDIT: Actually, I don't think we can generate any drop if both sides of the canyon are the same height. In-game, at least, the west side is lower, explaining the drop. I'm not sure where you got the drop you did - that would imply that gravitational potential energy was spontaneously generated during the fall! Let me check your figures.

EDIT 2: Oh, wait, I forgot Godot's shove. 4 meters per second initial velocity is a heck of a shove, which explains how she could end up over 2 meters above her original height.

This could make a good textbook problem, for a sufficiently dorky textbook.

That said, I think the main contribution to mean velocity is the length of time between murder and discovery. If we know the distance between the site of death and the final site, and we know how long it took for the corpse to be discovered, the average velocity is easy to find. Otherwise, we're stuck working out the length of time of each leg of the journey, and the velocity on each leg of the journey.
Re: Mobility: A Problem (MAJOR SPOILERS FOR ALL FIVE GAMES)Topic%20Title
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Detective 1: Well, I'd better be going.
Detective 2: So where's your car? I didn't see you drive here.
Detective 1: Oh, I just sit on top of the corpse and just wait for the killer to drag it away.
I'm gone for so long, and the colors got all psychedelic! Woohoo!
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