Question

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Who Killed Kenny At 2:45am on a night in 2006, Tammy, a maid who works in the house of multi-millionaire Kenny claims she was awoken by the sound of a loud thud outside her window. She got out of bed to cover that her employer had apparently fallen from one of his mansion's four balconies (1st, 2nd 3rd, and 4th floors). He was dead. Police arrived at 3:15am, and immediately noticed that Kenny was more than 7 feet horizontally away from the end of the balconies. Immediately the police sequestered those who were in the house that night; all are suspects in the murder. Police contacted Kenny's secretary, who was not at the house that evening, and obtained his schedule from the day before. Kenny had a dinner party the evening before. He had invited his friends, Mr. and Mrs. Jefferson. The Jefferson's arrived at 2pm and spent the hour between 3:30pm and 4:30pm alone with Kenny in a closed meeting over tea. Kenny's old business partner and his wife, Mr. and Mrs. Smith had arrived late to the dinner and spent an hour with Kenny privately over coffee after dinner between 9:00 and 10:00pm. As the CSI team arrived, the police began to interview the maid, Tammy. She told them that indeed Kenny hosted a dinner party that night. She had even prepared Kenny's favorite dessert rhubarb pie. In addition to the Smiths and Jefferson's, she indicated that Kenny's son John had also attended the dinner. John had arrived that morning. Kenny had some brandy with his son from 10:30pm to 11:30pm and had read alone in his study between the meeting with son and the Smith's According to Tammy, Kenny's evening had not been very eventful. She last seen him alive at 11:45pm when she brought him his medication with a glass of water, she indicated that he wasn't feeling well and he was running a fever of 100.2°F. At the time he was alone and was going to sleep. She also noted that he felt like he was burning up and elected to sleep with the doors to the th floor balcony opened that evening despite the cool temperature of 67.2°F. Additionally she indicated that the Smiths and Jefferson's slept that evening in the guest bedroom on the 2nd floor John slept on a cot in his father's 3'd floor, and she slept in the maids' quarters on the 1st floor. The detectives measured that each balcony is 10 feet in height from each other, and the deck of the 1st floor balcony is 5 feet above the ground Following Tammy's interview, the CSI team told detectives that it was definitely a murder; there were no bloodstains on the sidewalk where Kenny had landed. Given the injuries they determined that he had hit the ground with a velocity between 43 and 46 feet per second Aft er sealing off the house and sending Kenny to the morgue for further tests, the CSI crew left the ne around 6:30am and returned with more results at 10am. When they returned they told the suspects that toxicology results had left them puzzled. First they noted that the medical e xaminer had estimated the victim's core body temperature at 83.3°F at 4am and 75.2°F when they leaded him into the hearse at 6:15am. The toxicology reports indicated that 900mg of a poison with dissolution of 1/3 and absorption of 1/5 was prevalent in Kenny's sys tem and had been ingested metime in the past 24 hours. The poison had killed Kenny when the maximum dosage entered the bloodstream sometime after he was given the poison. From the information provided, conjecture as to who killed Kenny. What time did he die? When did the action that led to his death take place? From which balcony was he pushed of of? You must show all mathematical evidence to support your analysis. Some useful information: Newton's Law of Cooling The rate of change in the temperature dT/dt of an object is proportional to the difference between the Temperature T of the object and the Temperature To of the surrounding medium. Drug Dynamics The rate at which poison changes in the bloodstream (measured in mg/hr) once it is taken is given by the Differential Equation (DE). dy су Where: a dosage of poison b dissolution constant of the drug c- absorption constant of the drug Velocity locity of a falling object in ft/sec is given by the formula: The ve v(t)--32t +vo where, vít) is the velocity at time t, and vois the velocity at t o.

Answer 1

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