Part 3 Module 7 Real-world problems involving distance

Two useful facts From elementary geometry we have two familiar facts that can be useful if we are trying to calculate a distance. One of these is the Pythagorean Theorem, and the other is the formula for the circumference of a circle.

Exercise #1 The GEOMETRIZER The figure below shows an aerial view of The Hurl-O-Matic, a carnival ride in which the passengers are seated in a car, attached to the end of an arm which rotates rapidly around a central hub. Suppose that the length ( r ) of the arm is 39 feet, and that, at full speed, it takes 4 seconds for the car to complete one revolution. Find the speed of the car. A. 819 miles per hour B. 54 miles per hour C. 90 miles per hour D. 21 miles per hour E. 42 miles per hour

Exercise #2 The GEOMETRIZER Homer and Aristotle are loitering on a street corner when Plato, to whom they owe money, suddenly approaches. Homer begins running northward at 12 miles per hour, and Aristotle begins running eastward at 15 miles per hour. How far apart are Homer and Aristotle after 10 minutes? A. 1.6 miles B. 4.5 miles C. 3.2 miles D miles

Exercise #3 The GEOMETRIZER Archimedes is a traveling salesperson who needs to drive from Podunck to Boonies (see map below). However, Archimedes is too cheap to take the Boonies Expressway (which is a toll road), so instead he takes the Podunck Parkway to Sticks and then takes Sticks Highway to Boonies. The direct distance from Podunck to Boonies is 64 miles, and the distance from Sticks to Boonies is 45 miles. How much gas will Archimedes use, assuming his Yugo gets 5 miles per gallon? A. 9.1 gallons B gallons C gallons D gallons

Exercise from Part 3 Module 6 From The Big UNIT-izer How many square yards are in square feet? A B C D. 3888

Exercise #4 The GEOMETRIZER Study the race track shown below. If Gomer runs 32 laps around the track, how many miles will he have run? A miles B miles C miles D miles

Exercise #5 The GEOMETRIZER According to classical mythology, Sisyphus was condemned to spend eternity rolling a large rock up a hill. Upon reaching the top of the hill, the rock would roll down the other side, whereupon Sisyphus would repeat the process. Suppose the figure below (definitely not drawn to scale -- note the cosmic size of the hill) shows his situation. Suppose also that the rock is roughly circular with a diameter of 3.6 feet, and that on average it takes him 10 months to roll the rock one complete revolution. How long will it take him to roll the rock to the top of the hill? A years B years C years D years E years