Expert: Ahmed Salami - 10/11/2004

Question
Advanced Math Project #1
Jethro and the Home Video

Jethro was driving his pickup truck down a residential street one afiernoon (speed limit 3$ MPH) when he hit ice and ran into a telephone pole. Shortly thereafter, he was arrested and charged with speeding. You are investigating the case. Here are the facts so far

I.   Jethro never slowed down before hitting the pole. When he did bit the pole, his foot became wedged between the gas pedal and some debris, so the wheels of his truck kept rotating at the rate that they were moving before he bit the pole.

2.   Cfficer Battle, who was on helicopter traffic patrol, had been hovering above the scene of the accident. He was playing with some of the fancy equipment when Jethro began to slide off the road. According to Officer Battle, Jethro traveled 200 feet in 3 seconds.

3   Billy Bob was standing in his front yard at the time of the accident, making a home videotape of his little sister, Sissy, gargling to the tune of"Qilligan's Island." Later, while viewing the videotape and preparing to send it to America 's Funniest Home Videos) Billy Bob observed that the accident was recorded in the background of the videotape. He timed Sissy's performance to be iS se~nds long. Then by running the videotape in slow motion, he was able to Count the 24-inch diameter tires of Jethro's truck rotating 101 times while Sissy gargled.

Your job is to evaluate the testimony of Officer Battle and the evidence from Billy Bob's tape to decide whether you would rather be a defense lawyer or a prosecutor for this case. Then write your case for court, being sure to explain what these two pieces of information indicate to the jury; that is, you need to show 811 your mNthelnjltip in the body of your discussion  as explained by an expert. If either piece of testimony, or both, fails to support your claim, indicate why vou t~~:'~k that the witness is incorrect or unbelievable. You may be as creative as you wish as Ion; ~ you do not contradict any information given.

You may work with a partner or cons~tant on doing the mathematics, but you must write your own story. Ths project is worth 30 points as follows:
  18 points   Mathematical accuracy and Completeness
  6 points   Logical analysis of problem
  3 points   Nearness, grammar, spelling
  3 points   Creativity


Answer
Hi rt,
Sorry about the delay.
I'll only help with the obvious maths involved.
According to the officer, the truck was moving at
(200/3)ft/s = 66.67ft/s
From Billy's testimony(i'm assuming his sister's performance took 15 seconds because some of the things you typed are unclear to read), the truck was moving at
101/15 rev/s = 6.73rev/s
            = 42.3rad/s
the actual linear velocity being
(24/2).(42.3) = 507.6 inch/s
But 1 inch/s = 0.083 ft/s
507.6 inch/s = 42.3 ft/s
So the value of the speed as given by the officer is rather higher. Now, if the speed limit is
30 miles/hr = 44 ft/s
the truck hasn't gone beyond speed limits and hence cannot be charged with overspeeding. So i'll rather be a defense lawyer on this one.
I'm afraid i can only help you with the maths here. But feel free to get back to me whenever you feel there's the need.
Good luck.
Regards.