Who killed Meredith Kercher? part 23

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Numbers said:
This post is intended as an investigation of what can be learned about the window breakage using elementary Newtonian physics. The specific goal is to estimate a minimum velocity the rock would need to break the window and produce a distribution of shards within the room.

The first task of a rock thrower seeking to break a window, or a baseball pitcher aiming to strike out a batter, is to get the thrown rock or baseball to the target area, which is some distance away. For the baseball pitcher, this means getting the ball within the strike zone over home plate - a distance of 60.6 feet (about 18.4 meters) from the pitcher's plate on the pitching mound. For the rock thrower, this means throwing a rock of mass 4 kg from his position on the rampart facing Filomena Romelli's window to the window 3 meters (about 10 feet) away, with enough velocity for the rock to break the window.

One important principle of physics many of us learn from experience is that if one is throwing an object to reach a target some distance away, the object must be thrown hard enough – that is, for it to go fast enough – to cover the distance. Otherwise, the object will fall to the ground (or floor, if one is indoors) before reaching the target, because of earth's gravity.

Elementary Newtonian physics gives a method to calculate what the minimum velocity the thrown object must have to reach the target. The method is based on the observations that the time required for a thrown object (with a non-zero velocity relative to the earth's surface) to fall is the same as the time required for that object (with no velocity relative to the earth's surface) to fall, when air resistance (drag) and lift are negligible, or may be ignored. The situation of the object falling only under the force of gravity is called free-fall and the method is summarized online in:

http://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations-and-Free-Fall

Assumptions
1. The rock thrower is, of course, tall enough and with a good enough throwing arm to accomplish the task. The rock is thrown over-hand, with the arm extended above the head, and gripped somewhat like an American football rather than a baseball, with the ground of the rampart a distance d = -2 m from the vertical position of the rock when it is launched.
2. The effects of air resistance (drag) and lift, if any, on the rock will not be considered for the first estimate.
3. The acceleration of gravity near the earth's surface, g, is the generally used value: g = -9.8 m/s^2; see: https://en.wikipedia.org/wiki/Gravity_of_Earth
4. The rock must travel a minimum horizontal distance L = 3.5m; this value of L includes a “safety factor” of 0.5m intended to assure that the rock has enough horizontal velocity to penetrate the window glass at 3.0m from the thrower. The value of 3m is from the testimony of Marshal Francesco Pasquali.


Calculation of the free-fall time, t

t = square_root(2d/g)
t = square_root(2*(-2m)/(-9.8m/s^2))
t = 0.639s

Calculation of the average horizontal velocity, v_r-h-avg of the rock

v_r-h-avg = L/t
v_r-h-avg = 3.5m/0.639s
v_r-h-avg = 5.5m/s

Thus, the minimum horizontal velocity of the rock at launch, assuming negligible air resistance on the rock in its short flight, is the modest value of

5.5m/s = 19.7km/h = 12.3miles/h.

While Marshal Pasquali apparently did not measure the rock's velocity in his 3 test trials performed from 3m away from the test window, the window was indeed broken on each trial, and the glass shard pattern produced in the room was qualitatively similar to the one in Romelli's room as photographed by the police. Marshal Pasquali's work by itself establishes that there was no objective support for the allegation of the police that the break-in had been staged with the rock thrown within the room.
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Someone throwing over arm is not using horizontal velocity.

Interesting you refer to gravitational force as when I gave you the equation for this, you claimed to be baffled and had to resort to Shakespeare.
 
bagels said:
The prosecution didn't even try to get a fake expert to back up their claims of the rock being thrown from inside lol. It was basically "Yeah the defense has re-creations and the laws of physics...but look at that American **** sitting over there....come on....i mean come on people..." And Massei was like, the man has a point.
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LOL. Imagine the fascist cops picking on the American **** instead of the African drifter. Now there's a turnaround.
 
Numbers said:
The PGP has found out that Newton was part of the Masonic Mafia Marriott conspiracy supporting Knox and Sollecito.
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According to Dan Brown (or Tom Hanks, if you've seen the film), both Isaac Newton and Da Vinci were Grand Masters.

Maybe Dan Brown will appeal to you more than mind scrambling physics..? ;)
 
abaddon said:
Where dose the horizontal speed come from in an over arm throw in that case?
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It comes from throwing in an upward thrust by throwing at an upward angle. this is why you need to calculate the parabolic height and factor it in as to how it will fall and at what impact.

It is all to do with angles.
 
Vixen said:
It comes from throwing in an upward thrust by throwing at an upward angle. this is why you need to calculate the parabolic height and factor it in as to how it will fall and at what impact.

It is all to do with angles.
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I'm sure you will be able in that case to provide the supporting math, right? I mean, you obviously have worked this out, right?
 
Vixen said:
It comes from throwing in an upward thrust by throwing at an upward angle. this is why you need to calculate the parabolic height and factor it in as to how it will fall and at what impact.

It is all to do with angles.
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What if I throw a projectile straight up? Then what?
 
The PGP descend into self-parody when their ignorance of science and bias are exposed.

If a thrown object is given a vertical as well as a horizontal component of velocity, these components are orthogonal and are analyzed using an equation of motion for each orthogonal direction.

A positive component of velocity at launch in the upward direction will increase the time that the object would be in the air, but will not change the velocity at launch in the horizontal direction - unless the total magnitude of the velocity must remain constant, as in firing an artillery piece. Thus, launching an object, such as a football, artillery shell, or rock at an angle (greater than 0 degrees but less than or equal to 45 degrees) to the horizontal will potentially increase the horizontal distance (range) traveled by the object. That is why, for example, artillery officers want to know the range to the target and adjust the angle to the horizontal of the weapon's barrel to achieve that range, considering also that the exit magnitude of velocity of the shell is constant for a particular propellant charge.

Overhand throws may be made with the velocity of the object parallel to the ground; it's all in the motion of the wrist and arm. One could launch an object upward, downward, or straight ahead, based on release angle. Source: American football

Therefore, assuming that the time available for the travel of the rock is only that for free-fall from the launch position gives the minimum time of travel and the appropriate* minimum range, and is conservative.
*The true minimum range would be achieved by throwing the rock with only a vertical velocity, so that it would come down where it was launched. This upward toss may be the PGP approach to playing such games as baseball, cricket, or football. As a PGP pitcher would say to a batter: "Gee, I threw the ball but it didn't go toward you, it just hit me in the head."
 
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abaddon said:
I'm sure you will be able in that case to provide the supporting math, right? I mean, you obviously have worked this out, right?
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Picture a marble rolling along the ground, or a football. That is what horizontal velocity illustrates.

Not very useful for determining the impact of someone throwing an object through the air for maximum impact.

Anyone who has ever fielded will know that a well-hit ball will come down hurtling at an alarming speed towards one, making it hard to catch. This is because a good batsman has the skill to angle the ball at the right velocity and height to gain optimal advantage. Likewise, a burglar aiming a trajectory will want to optimise breaking a window pane effectively.
 
Apparently the PGP have never seen - much less played - baseball or softball, or American football (touch football, the wimpy version, uses tagging the ball-carrier rather than tackling).

Balls are thrown to other players using a horizontal velocity. Long-distance passes in (American) football are thrown at an angle to the horizontal, and the receiver actively positions to catch the ball. It should be pointed out that in American professional football, the grid (yard lines) are 10 yards = 30 feet - somewhat less than 10 meters - apart, and a pass of that distance would be launched horizontally (an angled pass would be used only to prevent interception by an opposing player).

The rock in this case needed to travel only 3 meters - about 10 feet - to hit the window.
 
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Numbers said:
Apparently the PGP have never seen - much less played - baseball or softball, or American football (touch football, the wimpy version, uses tagging the ball-carrier rather than tackling).

Balls are thrown to other players using a horizontal velocity. Long-distance passes in (American) football are thrown at an angle to the horizontal, and the receiver actively positions to catch the ball. It should be pointed out that in American professional football, the grid (yard lines) are 10 yards = 30 feet - somewhat less than 10 meters - apart, and a pass of that distance would be launched horizontally (an angled pass would be used only to prevent interception by an opposing player).

The rock in this case needed to travel only 3 meters - about 10 feet - to hit the window.
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I have played rounders and pesäpallo (similar to baseball). At school I was made to play hockey and can vouch for its lethality should you get wacked by either the hockey stick or the ball.

No, horizontal velocity is to do with sports such as ice hockey.

In any case, velocity is only of interest in the Kercher case as a means of determining the impact of the boulder. What we are really interested in is the force.

Would someone like slenderly- built Rudy have the capacity or skill to whizz a sandstone slab through a window about four feet above his height, from nine to ten feet away - first time - with enough strength to force the window and inner shutters open to sixty degrees and with a shard of glass embedded within the wood of the shutter and with no back fall of glass into the garden below or windowsill outside.

If thrown from indoors, then it is more of a horizontal approximation and of a greater impact.

In any case, whilst bricks might be a favourite of smash and grab robbers of shop windows, leaving a big hole as it does, I can't see a stealthy backstreet burglar in the hinterlands will want to cause an almighty crash, alarm the neighbours and risk the rock simply bouncing off the wall down into the garden below. A medium sized stone at optimal velocity will do the trick with minimal noise and more accuracy.

The PIP theory Rudy wanted to make a row so that he could see if there was any response. So, not only is Rudy a master rock climber and super bowler rock slinger, he's also incredibly dumb! Going off for a kebab and coming back later to climb in.
 
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abaddon said:
How could it acquire any horizontal speed? According to you that is impossible.
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Try it for yourself. A ball thrown straight up into the air has little power, little distance and the only force acting on it is gravity, which is why we can use the law of gravity to calculate its pound-force.
 
Vixen said:
Try it for yourself. A ball thrown straight up into the air has little power, little distance and the only force acting on it is gravity, which is why we can use the law of gravity to calculate its pound-force.
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OK. And if one throws horizontally or at an angle, what forces are in play?
 
Vixen said:
LOL. Imagine the fascist cops picking on the American **** instead of the African drifter. Now there's a turnaround.
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The African drifter didn't horribly embarrass them on a global stage by having the nerve to be innocent despite their most excellent pizza-watching detective skills :p
 
Vixen said:
I did not say it was impossible. I said it was improbable (as did all the courts, apart from crooked Hellmann [torn to shreds by the Supreme Court]).

Still no proof 'it was Rudy wot done it'.
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This is what the courts said happened:

UojNsnx.jpg


Which is why Amanda is free in Seattle, and you're here refusing to accept my challenge of quoting my image and saying "that is an accurate illustration of what happened."
 
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