2011 Excellence in Mathematics Contest Team Project Level I (Precalculus and above) School Name: Group Members:

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1 011 Excellence in Mathematics Contest Team Project Level I (Precalculus and above) School Name: Group Members:

2 Reference Sheet Formulas and Facts You may need to use some of the following formulas and facts in working through this project. You may not need to use every formula or each fact. A bh C l w A r Area of a rectangle Perimeter of a rectangle Area of a circle 1 y y C r A bh m x x Circumference of a circle Area of a triangle Slope 1 1 a b c 580 feet = 1 mile Pythagorean Theorem h( t) 16t v0t h 0 Height of a free falling object: y Asin( B( x C)) D.54 centimeters = 1 inch b s 1 f ( x) dx y Acos( B( x C)) D Arc length a 1 kilogram =. pounds 1 ton = 000 pounds 1 gigabyte = 1000 megabytes 1 mile = 1609 meters 1 gallon = 3.8 liters 1 square mile = 640 acres 1 sq. yd. = 9 sq. ft 1 cu. ft. of water = 7.48 gallons 1 ml = 1 cu. cm. 4 3 V r h V Area of Base height V r 3 Volume of cylinder Volume Volume of a sphere Lateral SA = r h Lateral surface area of cylinder b b 4ac x a Quadratic Formula tan sin cos References:

3 TEAM PROJECT Level II 011 Excellence in Mathematics Contest The Team Project is a group activity in which the students are presented an open ended, problem situation relating to a specific theme. The team members are to solve the problems and write a narrative about the theme which answers all the mathematical questions posed. Teams are graded on accuracy of mathematical content, clarity of explanations, and creativity in their narrative. We encourage the use of a graphing calculator. America s Got Talent In a recent season of the television show America s Got Talent, a contestant going by the name of Professor Splash dove from a height of 6 feet into a kiddy pool containing only 1 inches of water. He survived and is now considering a more complicated and exciting stunt.* This time, Professor Splash will dive from a moving Ferris wheel into a tub of water that is on a moving cart that runs along a track parallel to the plane of the Ferris wheel. His team of experts will attach a diver s platform to one of the seats on the Ferris wheel. As the Ferris wheel turns, an assistant holds Professor Splash by the ankles. The assistant must let go at exactly the right moment, so that the Professor Splash will land in the moving tub of water with a spectacular SPLASH. In this project, you will investigate this situation and provide the needed analysis so that the assistant will indeed let go at the appropriate time so that we see and hear a SPLASH and not a SPLAT! Part I Making Sense of the Situation Provided below are all the necessary details so that you can solve this problem. The Ferris wheel has a radius of 50 feet. The center of the Ferris wheel is 65 feet off the ground. The Ferris wheel turns at a constant speed, making a complete turn every 40 seconds. The Ferris wheel turns counterclockwise. When the cart starts moving, it is 40 feet to the left of the center of the base of the Ferris wheel. The cart travels to the right at a constant speed of 15 feet per second. The water level in the cart is 8 feet above the ground. When the cart starts moving, the diver s platform is at the 3 o clock position in its cycle. Sketch a picture of the situation. Label the measurements given and show where the diver begins the stunt. Be sure to show where the cart is at the beginning of the stunt. * This is a hypothetical situation. While Professor Splash did indeed compete on America s Got Talent, he is likely not contemplating the stunt proposed here. 3

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5 Part II Solving the Problem Hopefully, you are now ready to solve the problem. It is a pretty big problem to solve with many aspects and subparts to consider. You may feel like you just want to dive in (ha! Get it?) and get to work. However, you might also feel like you need some guidance. Maybe you don t need guidance right now or maybe you do. Either way, below is a list of things to consider in solving this problem. Determine a function formula for the diver s height above the water level at the time of release Determine a function formula for the diver s x-coordinate at the time of release Determine a function formula for the vertical component of the diver s velocity when he is released Determine a function formula for the horizontal component of the diver s velocity when he is released Determine the duration of the diver s fall from the time of release until he reaches the water level Determine the total time the cart is moving Determine the x-coordinate of the cart at the time the diver reaches the water level Determine the x-coordinate of the diver when he reaches the water level As you work through the project, you may want to refer back to this page. Even if you are not able to solve the problem in its entirety, you may address some of these items for increasing your chances of competing in the contest. Using the paper provided, provide a neat, clear, and as complete a solution as possible that can be judged for the competition. 5