2009 Excellence in Mathematics Contest Team Project Level II (below Precalculus) School Name: Group Members:

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Ilene Lang
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1 2009 Excellence in Mathematics Contest Team Project Level II (below Precalculus) School Name: Group Members:

2 SUDDEN IMPACT: THE SUSPECTS The Suspects Gil Bates CEO of Macrohard Corporation and software king-pin. Lives in a waterfront mansion on Puget Sound. Threatened to eliminate Mousehand after discovering trade secrets were being leaked to Pear Computing. Debra Downtime Anarchy activist and renegade author of deadly computer viruses. Low-level programmer on Macrohard s Operating System Door 99 and long-time lover of Tim Witt. In recent months, however, she had shown a romantic interest in Dudley Mousehand although they frequently and violently quarreled. Tim Witt Head of DIM Computing, a lead publisher of antivirus software. Long-time lover of Debra Downtime: however, in recent months he d been losing ground to Dudley Mousehand. He and Mousehand had engaged in a brief skirmish at a Macrohard reception. Nick Smythe Former security guard at Macrohard Corporation. Discovered secret Pear Computing documents while searching Mousehand s suitcase during a spot security check. Informed his daughter, an advertising executive at Pear Computing. Mousehand was fired shortly thereafter. Mousehand had threatened to squash Smythe like a fly after being fired from Pear Computing. Smythe departed early the afternoon of Mousehand s death. 2

3 SUDDEN IMPACT: FALLING BODY Chief Investigator, Sally Sleuth has come to you for technical assistance. The coroner has released his preliminary report. Based on the damage to Mousehand s body, it appears that he struck the ground at a speed between ft/sec. (The velocity of a falling body with initial velocity of zero (neglecting air resistance) is v 32t where t is time in seconds. Note: a negative velocity indicates a falling body and a positive velocity indicates a rising body.) 1. Determine how long Mousehand had been falling when he struck the ground. 2. Determine the approximate distance Mousehand had fallen when he struck the ground. (The 2 vertical distance a falling object has traveled at time t seconds is modeled by s v0t 16t where v 0 is the initial velocity.) 3

4 SUDDEN IMPACT: IMPACT VELOCITY Chief Investigator, Sally Sleuth, has again come to you for technical assistance. Detectives have determined that although Gil Bates had been tied up in meetings until 2:30 pm, he was in his office at the purported time of the alleged crime. Debra Downtime alleges she was in her office as well but detectives have been unable to substantiate her claim. Both Bates and Downtime claim to have been alone. Bates office is 346 feet above the ground, Mousehand s office is 306 feet above the ground, and Downtimes office is 266 feet above the ground. Outdoor security cameras captured images of Mousehand as he fell. Image analysis indicated that he was at 206 feet at 15:22.02 and 110 feet at 15: (Hint: 2 s 16t v0t s 0 where 0 v is initial velocity and s 0 is initial height.) 1. Determine from which office he fell 2. Calculate his velocity at impact. Does this substantiate the coroner s report that the velocity of impact was between 125 and 150 ft/sec? 3. Determine whether your results have cleared any of the murder suspects. 4

5 SUDDEN IMPACT: AGE OF ART Chief Investigator, Sally Sleuth, has again come to you for technical assistance. Detectives have discovered that the famous Van Gogh painting, Starry Night, has been stolen. The painting, which had been loaned to Mousehand by The Museum of Modern Art in return for a $750,000 contribution, vanished from his office on the day of his death. A search of Tim Witt s condominium turned up a painting that appears to be the stolen art work. Witt claims that the painting is a replica, not the original. He said he purchased the work as a gift for Downtime and had intended to give it to her during the 3 pm ribbon-cutting ceremony for his new building, DIM Towers, on the day of the crime. However, Downtime stood him up. Witt presented detectives with a hand-written sales receipt from a Seattle art dealer date/time stamped: 08/11/09 13:52:46. The dealer says he sold a Starry Night replica to Witt sometime in the afternoon of August 11, 2009, but refused to disclose any other details. Due to his extensive criminal history, the dealer s credibility is questionable. Scientific analysis of the painting revealed that it contains 99.2% of its original carbon-14 (half-life 5730 years). The original painting was completed in June Determine if the painting in Witt s possession is an original or a replica. 2. Determine whether your results have cleared any of the murder suspects. 5

6 SUDDEN IMPACT: ART AUCTION Detectives believe that one of the murder suspects has the stolen Van Gogh painting, Starry Night, and will attempt to sell it on the black market. The periodic underground art auction is to be held in Pikes Place Market tomorrow night at 11 pm. In an interview with detectives, Nick Smythe s daughter reluctantly revealed that her father had incurred a $400,000 gambling debt. Mobsters have given him 31 days from today to pay off the debt. Furthermore, he depleted his life savings paying for his late wife s cancer treatments and has been living month to month on his income from Macrohard. Detectives speculate that if Smythe is the thief (and possible killer) he will attempt to raise money by selling the painting. Black market financial experts estimate that the painting will generate between $300,000 and $500,000. They told Sleuth that the amount of revenue the painting should generate is proportional to the difference between 1 and the reciprocal of the fourth root of the number of auction attendees. A painting of similar quality sold at last month s auction for $375,000. There were 256 people in attendance. 1. Determine the minimum auction attendance necessary to generate $400, Determine whether your results have cleared any of the murder suspects. 6

7 SUDDEN IMPACT: TIME OF DEATH The coroner s office has informed Sally Sleuth that Mousehand did not die as a result of the injuries sustained by the fall. He was already dead. Mousehand had sustained 29 bee stings on the chest and gone into anaphylactic shock and died of cardiac arrest. Blood tests further revealed that he was heavily sedated at the time. Detectives discovered traces of Valium in a wineglass left on the floor of his office. Detectives have confiscated the computers of Downtime, Mousehand, and Smythe. Mousehand sent the following to Downtime at 2:01 pm. She had not yet read it when her computer was confiscated. My love, Am looking forward to our rendezvous this afternoon. Will meet you at Ivar s instead of Pier 51 on the waterfront at 4 pm. Thought we might catch an early movie after dinner. Am still angry with Smythe for getting me fired. Think I ll call him into my office and give him a piece of my mind. I d love to toss him out of my life. BTW, my computer has been acting up. Might be a virus. When you get a chance, come have a look. Yours Truly, Fingers Smythe returned from a going away luncheon for one of his subordinates at 2:05 pm. He received the following from Mousehand at 2:07 pm. Mr. Smythe: I am concerned with the security situation in my office. Even though my Van Gogh painting is encased in glass, I do not feel secure. Meet me in my office at 3 pm to discuss security. Mr. Mousehand 7

8 Mousehand s computer was inoperable due to irreparable damage caused by a computer virus so detectives were unable to extract any additional information from it. Smythe reported to Mousehand s office as directed at 3 pm and claims that when he entered the office he found Mousehand lying on the floor. He says he immediately felt light headed and passed out. When he regained consciousness, he discovered that the body of Mousehand had vanished. He claims he got spooked and fled to his daughter s office at Pear Computing. Many of the investigative team believe Smythe is the killer; however, Sleuth believes that Downtime is the culprit. Unfortunately, she has been unable to come up with any evidence to clear Smythe; however, the coroner just released some information that she thinks you may be able to use to vindicate him. At 4:22 pm, Mousehand s body temperature was 93.4 F and 5:22 pm it was 91.6 F. The temperature inside of Mousehand s office and outside the Macrohard Corporate Center from 1 6 pm was 68 F. 1. Determine the time of death of Mousehand. Assume his temperature at the time of death t was 98.6 F. The formula for body temperature T at time t hours is T 30.6e Determine whether your results have cleared any of the murder suspects. 3. Who killed Dudley Finger Mousehand? 8

3. Each quarter weighs 0.2 ounces. How much money has been stolen from the bank?

3. Each quarter weighs 0.2 ounces. How much money has been stolen from the bank? Name: Bell: Clues Sheet Dear Detective, Someone has robbed the National Bank in Washington D.C. It is your job to use the clues left by the perpetrators to locate and apprehend the robber. Your tools will