From: perlman@qso.Colorado.EDU (Eric S. Perlman)
Subject: Re: Lets do some stone physics ...
Organization: University of Colorado, Boulder
Date: Mon, 27 Jul 1992 21:57:19 GMT

In article <1992Jul24.020248.23277@wpi.WPI.EDU> nyh@emilio.WPI.EDU (Nevo Y Hed) writes:
>In article <1992Jul23.215254.16589@colorado.edu> 
>perlman@qso.Colorado.EDU (Eric S. Perlman) writes:
>[...]
>>The rocks I remember from the video looked to be 2-5 inches in diameter.
>>That still means a rock weighing 1-3 pounds (you're talking about
>>something the size of a baseball or softball but several times as
>>dense).  These thrown as hard as possible over a wall, and having a
>>20-30m drop down to the plaza in front of the wailing wall.  Considering
>>that fastballs which hit on the head can cause rather severe injuries,
>>and that these rocks are both heavier and have 20-30 meters of height,
>>that's a significant danger.  Not as significant as a bullet, but pretty
>>significant nevertheless.
>
>
>
>OK ... Lets make it more official - I have dran here [with my
>emacs-art talent] a description of the travel of a stone.  I am sure
>that there are many people here that are more experts then myself in
>physics.  I didn't trust myself with alculating V3y.  If noone will
>dare at this chalange I will lookup my physics book and try not to
>fu**up or ask my dad.  We also need astimates for V1x & V1y - I am
>taking Eric's etsimate for H - if you know a better number - go ahead.
>After we get a final number for |V3| we can then ask any ol' MD what
>it actually means if it hits someone in the head.
>
>
>
>
>	
>                        __--------__
>                      _-            -_
>  V1y                ~ 	              ~
>       	            '	               `       ---> V2x  |
>  ^       _        /                    \                |
>  |   V1  /|      /                      \     \         V V2y
>  |      /       /	                  \     \
>                /	                   \    _| V2
>      _  _  _  / _  _  _  _  _  _  _  _  _  \  _  _  _  _  _  _  _  _
>            o  	                       ^     \
>           '|` 	                ----   |      \
>           / \ 		       |    |  |       \
>          -----------------    |    |  |        \
>                               |    |  |         \
>        --->V1x 	            |  |H         \
>                                    |  |       	   \
>   _            	            |  |            \          |
>  |\            	            |  |             \         |
>    \           	            |  |              \	   \   V V3y
>     \          	            |  |               \    \
>      Al-Aqtza Mousq                |  |      ---> V3x  \    _| V3
>	                            |  |                 \
>	                            |  V                  o
>	          The Wall --->     |                    '|`
>	                            |                    / \
>   H   = 25m ?
>   V1x = ?
>   V1y = ?
>   V2y = V1y
>   V2x = V1x
>   |V2|= |V1|
>   V3x = V2x
>   V3y = ??
>   |V3|= Sqrt(V3x^2+V3y^2) = ??

Let's take a reasonable example.  Assume that V1x = 30 m/s (it sounds
like a lot, but this translates to a bit under 70 mph, and those who
know baseball know that the average major-league fastball is something
like 90 mph), and for simplicity, assume that V1y=V2y=0.  Then, since
any and all of V3y will be from gravity, we get, from simple
kinematics,  V3y=22.14m/s.  This gives |V3|=37.3 m/s, or nearly 86 mph
This is the *minimum* y-velocity case for this x-velocity; if V1y
is nonzero, the final velocity is also larger.  This last is
*significantly* more likely, especially since there's a wall to get
over.  

What this is telling us is that even a rock thrown by a small child from
25 m or so up acquires a lot of velocity and hence makes a pretty darned
significant impact upon an unknowing target.


-- 
"How sad to see/A model of decorum and tranquillity/become like any other sport
A battleground for rival ideologies to slug it out with glee." -Tim Rice,"Chess"
     Eric S. Perlman  <perlman@qso.colorado.edu> or <eric@lyra.Colorado.EDU> 
  Center for Astrophysics and Space Astronomy, University of Colorado, Boulder
Organization: Masters student, Information Networking Institute, Carnegie Mellon, Pittsburgh, PA