HW 6.1

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6.1: Angles and Their Measure Homework Name ________________ Date ___4/27/2020________ Period ____ 105. Bicycle Wheels The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 35 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning? 26/2 = 13 = radius 2(pi)(13) = 26(pi) in. 1 mi = 63360 in. 35 mph = 2,271,600 in/mi (60 mins) X = (2,217,600/60 mins)(26)(Pi) in. 452.69 revolutions per minute 107. Distance between Cities Memphis, Tennessee, is due north of New Orleans, Louisiana. Find the distance between Memphis (359’ north latitude) and New Orleans (2957’ north latitude). Assume that the radius of Earth is 3960 miles. The latitude of a location L is the angle formed by a ray drawn from the center of Earth to the Equator and a ray drawn from the center of Earth to L. See the Figure. Memphis is at 35 degrees north New Orleans is at 29 degrees North 113. Pulleys Two pulleys, one with radius 2 inches and the other with radius 8 inches, are connected by a belt. (See the figure.) If the 2- inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute of the 8-inch pulley. [Hint: The linear speeds of the pulleys are the same; both equal the speed of the belt.] 12pi = 8*x x = 12pi/8 ...... 3pi/2 (8 * 3pi/2 = 12pi) 12(pi) per min is the equivalent of 6 revolutions per minute
115. Computing the Speed of a River Current To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour. Radius = 4 ft 2(pi)(4) = 251.33 ft 10 x 251.33 = 2513.3 ft/minute 2513.3/5280 = 0.48 mi/h 118. Difference in Time of Sunrise Naples, Florida, is approximately 90 miles due west of Ft. Lauderdale. How much sooner would a person in Ft. Lauderdale first see the rising Sun than a person in Naples? [Hint: Consult the figure. When a person at Q sees the first rays of the Sun, a person at P is still in the dark. The person at P sees the first rays after Earth has rotated so that P is at the location Q. Now use the fact that at the latitude of Ft. Lauderdale, in 24 hours a length of arc of 2(3559) miles is subtended.] 90 miles x 24 hrs/2(pi)(3559) 2011546.8 miles 122. Nautical Miles A nautical mile equals the length of arc subtended by a central angle of 1 minute on a great circle* on the surface of Earth. (See the figure.) If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary, or statute, miles. *Any circle drawn on the surface of Earth that divides Earth into two equal hemispheres. 360 deg = 2(pi)rad 1 deg = (pi)/180 rad 60 min = (pi)/180 rad 1 min = (pi)/10800 rad S = (3960)(pi/10800) S = 1.15 miles 123. Approximating the Circumference of Earth Eratosthenes of Cyrene
(276–194 BC) was a Greek scholar who lived and worked in Cyrene and Alexandria. One day while visiting in Syene he noticed that the Sun’s rays shone directly down a well. On this date 1 year later, in Alexandria, which is 500 miles due north of Syene he measured the angle of the Sun to be about 7.2 degrees. See the figure. Use this information to approximate the radius and circumference of Earth. 360 / Arc Angle Circumference / 800km = 360 / 7.2 = 40,000km 40,000km/2 x 3.14 = r r = 6366.198 km
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