Raymond B. answered • 02/22/23
Math, microeconomics or criminal justice
1/2 mile south = s, s'=-35 mph (negative sign because the distance is getting shorter)
1/2 mile east = e, find e'= speed of the car
hypotenuse = sqr(1/2^2 + 1/2^2) sqr(2/2^2 = sqr2/2 = about 1.414/2 = about .707 miles
= distance between the two cars= h
h' = 20 mph
h^2 = s^2 +e^2
take the derivative with respect to time (measured in hours)
2hh' = 2ss' +2ee'
divide by 2
hh' = ss' + ee'
plug in the known values of h,h', s,s' and e
(sqr2)/2])(20) = (1/2)(-35) + (1/2)e'
solve for e' = speed of the car about to get a ticket or not
divide by 1/2
sqr2)(20) = -35 + e'
e' -35 = 20sqr2
e' = 20sqr2 +35
=about 20(1.414)+35
=about 28.28 +35
= about 63.28 mph
that's a caclulus answer. differential calculus is half of calculus. derivatives are differential calculus
or because there's a triangle involved, this could come under the category of trigonometry, the study of angles and triangles galore. "tri-angle" and "tri-gonometry" have that "tri" for 3.
3 sided polygon = a triangle
3 angles, like every triangle, one angle = 90 degrees, as this is a right triangle.
the other 2 angles are each 45 degrees. It's an isoscelese right triangle, with 2 sides equal, each 1/2 mile.
it's a triangle with sides in the ratio 1:1:sqr2. witch is also the ratio 1/2:1/2:sqr2/2
corresponding angles are in the ratio 45:45:90 which is the same as 1:1:2
That's the math answer. you can ignore what follows, unless you have nothing better to do than read it. IF you have nothing better to do, it must be a very slow boring day, or night. some people actually work these problems at 3am.
if the police are driving the speed limit of 35 mph
the driver will get pulled over, with a speeding ticket
and for 33 over the limit possible reckless driving citation and arrest
probably felony endangerment or felony flight
they'll probably charge him with a felony or two, then offer a plea deal for misdemeanor reckless. a public defender will advise taking the plea deal, to avoid risk of a felony
police car's radar may not have been calibrated, making the estimated speed more than actual
insurance premiium increases will make the lead foot very costly, possible license suspension
any alcohol on the driver's breath and add in a DUI charge too, with possible revoked licence.
if the driver is out of state, they'll have trouble defending the charges, which the police know, so they'll take on more charges. Even if a privately retained defense attorney gets an acquittal, the lawyers' fees get very expensive.
Economically, it's a Lose Lose situation, for the driver. Plus the car may get towed after an arrest, with civil forfeiture seizing the vehicle, auctioned off at a fake police auction where the police buy it at bargain basement prices. Some police even plant drugs in the car, pretend to find them, and tack on some drug charges on top of everything else. Some prosecutors know that, allow it and just say they'll drop the drug charges if you plead guilty to the other charges.
Welcome to what started out as a slight speeding ticket. Some towns raise money on traffic tickets, and put up surprise speed signs hidden by bushes. They're called speed traffics. check on line for them, if you plant trips to previously untraveled places.
even if it's just a minor speeding ticket, 99.9% of traffic cases, the traffic judge finds you guilty or responsible, and tacks on a bigger fine for taking up his time in court. Routine to punish defendants for going to trial.
going nearly twice the speed limit will be like going 130 mph on a highway with 65 mph limit.
You're toast at a trial, as the prosecutor conjures up images of dead people, mangled bodies in accidents, and even may file attempted murder charges.
UNless you can get the personnel file of the police and see how many others he's framed, talk to them, get them as witnesses as to how they got screwed royally.
or math wise
look at the 35 and 20 mph sides
double them to get 70 and 40
they're in a 7 to 4 ratio
7^2 +4^2= 49+16= 65
that 65 is very close to the speed of the east bound driver =63.28
If you stayed up until 3am to 4am working on this or thinking through the legal financial consequences, go to sleep, and dream about the numbers. Some of the best math is when you're asleep. Some people count sheep. Others do calculus or trig in their sleep. dreams are a mixed bag of seemingly unrelated things, that show up in weird patterns. Then math numbers show up in weird connections you never thought of, all just delivered to you relatively stress free. When you wake up, write down your math dreams before you forget them. Never know if they hit on something.
