November 21, 2003

Dear Myron,

You have asked me to figure out if Roger Driver was the one who is responsible for the death of Mr. Gusterson and if Victor Dendron was implicated in any way in the death of Mr. Gusterson.

I have found that the sack of lead shot that killed Mr. Gusterson was dropped from 67 feet above the ground, which is not anywhere near where Roger Driver's apartment is located, on the 9th floor. On another hand, the sack did come from the area of Victor's apartment on the 7th floor, and he could be responsible for the death of Mr. Gusterson.

First off, I am not saying that Victor is the one who killed Mr. Gusterson and that Roger Driver is not responsible for his death, due to several situations. For one, Victor might not have been at his apartment that day and someone could have placed the bag of lead shot. Also my calculations do not factor in the air resistance or the time it may have taken for the sack to be released from where it was situated. So based on the air resistance, this would make the sack seem as if it were dropped from a higher height. When in actuality it may have come from a lower floor, which is the reason why I am pretty sure Rodger Driver is not responsible for the death of Mr. Gusterson. We also cannot be sure if the clock, which Mr. Gusterson installed, was stopped due to the force of the lead shot hitting the ground. Even if this happened the clock may have taken sometime to stop completely after the incident. Another thing is that the building may not have been 90 feet high. It could have been a little higher or a little lower, so you cannot be really sure how high it is. The same also goes for the height of each floor, which is assumed to be 10 feet, when each floor could be a different height. It is also possible that the alarm is not what released the bag. Someone could just have dropped it, which would totally change the answer. Finally the height of Mr. Gusterson could have thrown off the calculations because I am not sure if the sack turned off the alarm when it hit the ground or Mr. Gusterson.

I figured out that the bag was dropped from a height of 67 feet by first looking at the two clocks. The alarm was turned off at 6:52:23:63 am and then the clock was stopped at 6:51:25:67 am. The difference between the two clocks is 2.04 seconds. Since I know that gravity is 32.2 ft/sec² (or as you may know it to be 9.8 m/sec²), I was able to figure out the height at which the bag of lead shot was dropped based on the physics formula,

I found this formula on page 58 from the book, of ìPrinciples of Physics.î So for the formula, I plugged in 32.2 m/s for the gravity, and for the time I plugged in 2.04 seconds. The answer that the formula gave me is that the sack was dropped 67 feet up.

Another way in which I looked at the problem is graphically. Plugging in the formula above into my calculator does this. The graph of this formula can be seen in figure 1, on the top of page 3.

On the graph you see that the time axis goes from 0 to 2.04 seconds, which is the time it took the sack to fall. Then on the velocity axis you can see it goes from 0, which is the velocity when the sack started falling, to 65.7 ft/sec, which is the velocity of the sack after 2.04 seconds, when it hit the ground. Another thing is that the slope of the line on the graph is equal to the gravity, which we know as a constant of 32.2 ft/sec². So in Chapter 5, of the textbook, Single Variable: Calculus, I learned that the area under the curve is equal to the distance traveled by the sack of lead shot. So to find the area I used the formula for the area of a triangle,

The base is seen to be 2.04 feet and the height is 65.7 ft/sec. The answer for the area also comes out also to be 67 feet, which is the distance the sack was dropped from.

Since I now know the distance that the sack was dropped from, I decided that it came from Victor's apartment on the second floor because his apartment starts at 60 feet high and goes to 70 feet high. I concluded this based on the fact that the hardware store goes from 0 feet to 10 feet, Mr. Gusterson's apartment from 10 feet to 20 feet, Mr. Smith's apartment from 20 feet to 30 feet and so on until we get to Victor's. This also proves that it could not have come from Roger Driver's apartment, which extends from 80 to 90 feet high.

I hope that this information is helpful to you and will finally solve the case in the death of your beloved friend Mr. Gusterson. I would also like to mention that I received help from the book, Principles of Physics, on page 58 and from the Single Variable: Calculus book, in chapter five. Dr. Crannell also proofread my paper and I received help from Andrew. Finally I would like to wish good luck in your quest and please let me know what happens in the future with the case and with Philomena.

Sincerely,

Brian Maksimak