[Prev][Next][Index][Thread]

Re : Fighting a ticket

Dear Juan,

The problem is not so easy : you have to know how far away from you he was
when he was driving Ymph, and you Xmph. In first approximation, we suppose
you know that distance.

For instance, let suppose that he was A mile(s) behind you. The formula
are :

time (in sec.)  = A / (Y-X) * 3600
distance (HIS)  = time * Y / 3600     (in Miles)
distance (YOUR) = time * X / 3600     (in Miles)

Application : if he was 1/4 (0.25) mile behind you when you were driving
80 mph and he was 105 mph, then he needs :

time = 0.25 / (105 - 80) * 3600 = 36. sec.   to reach you.

During that time, he did : 36 * 105 / 3600 = 1.05 mile
and you did              : 36 *  80 / 3600 = 0.80 mile
(and the difference is ok : 0.25 = 1/4 mile).


Now, lets estimate how far away he was from you (i.e. A). We suppose that :

- - 1) he just started when you passed him
- - 2) he needs B sec. to reach Y mph
- - 3) he accelerates 'linearly'. That's not right, for sure (...), and
     that means we will slightly sur-estimate the distance between you and him.
     
Now, the formula is :

1) he needs :
              distance (in mile) = B * (Y/2) / 3600
   to reach Y mph
   
2) during that time, you did :
              distance (in mile) = B * X / 3600
              
So, the difference gives you the distance between you and him :

          Distance  A  = B * (X - Y/2) / 3600 (in Mile)
          
          
Application : if he needs 26 sec. to reach 105, and you were driving 80
mph, then :
            A = 26 * (80 - 105/2) /3600 = 0.198 Mile
                                            
Now, you can report that value in the first formula :

	time = 0.198 / (105 - 80) * 3600 = 28.5 sec.  to reach you
	
and he did, from the start to the point where he reached you :

        distance = 26 * (105/2) / 3600 + 28.5 * 105 /3600
                 = 1.21 Mile
                 

Hope it helps ...


Damien Veyret