PAP PRECALCULUS LS 4-1B

  1. The minute hand of a clock is 6 inches long. How far does the tip of the minute hand move in 15 minutes? In 25 minutes?

15 min______

25min______

  1. A pendulum swings through an angle of 20° each second. If the pendulum is 40 inches long, how far does its tip move each second?

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  1. Find the area of a sector of a circle of radius 4 metersformed by an angle of 45°. Round answer to two decimal places.

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  1. A water sprinkler sprays water over a distance of 30 feet while rotating through an angle of 135°. What area of lawn receives water?

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  1. An object is traveling around a circle with a radius of 5 centimeters, If in 20 seconds a central angle of 1/3 radian is swept out,what is the angular speed of the object and what is its linear speed?

Angularspeed______

Linear speed______

  1. 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?

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Name______

  1. The radius of each wheel of a car is 15 inches. If the wheels are turning at the rate of 3 revolutions per second, how fast is the car moving in inches per second and in miles per hour?

in/sec ______

mph ______

  1. Memphis, TN is due north of New Orleans, LA. Find the distance between Memphis (35°9’north latitude) and New Orleans (29°57’ north latitude). Assume the radius of Earth is 3960 miles.

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  1. Charleston, WV is due north of Jacksonville, FL. Find the distance between Charleston (38°21’ north latitude) and Jacksonville (30°20’ north latitude.) Assume the radius of Earth is 3960 miles.

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  1. Earth rotates on an axis through its poles. The distance from the axis to a location on Earth 30° north latitude is about 3429.5 miles. Therefore, a location on Earth at 30° north latitude is spinning on a circle of radius 3429.5 miles. Compute the linear speed on the surface of Earth at 30°.

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  1. The mean distance of the Moon from Earth is 2.39x105 miles. Assuming that the orbit of the Moon around Earth is circular and 1 revolution takes 27.3 days, find the linear speed of the Moon in miles per hour.

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  1. A neighborhood carnival has a Ferris wheel whose radius is 30 feet. You measure the time it takes for one revolution to be 70 seconds. What is the linear speed in feet per second of this Ferris wheel? What is the angular speed in radians per second?

Linear speed______

Angular speed______

  1. 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 in miles per hour?

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  1. A spin balancer rotates the wheel of a car at 480 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed (mph) is being tested? At how many revolutions should the balancer be set to test a road speed of 80 miles perhour?

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  1. At the Cable Car Museum you can see the four cable lines that are used to pull cable cars up and down thehills of San Francisco. Each cable travels at a speed of 9.55 miles per hour, caused by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating in revolutions perminute?

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  1. 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. If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary statute miles.

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  1. Eratosthenes of Cyrene was a Greek scholar who lived and worked in Cyrene and Alexandria. One day while visiting in Cyrene he noticed that the sun’s rays shone directly down a well. On this date 1 year later, in Alexandria, which is 5oo miles due north of Cyrene he measured the angle of the sun to be about 7.2 degrees. Using this date, what did heapproximate the radius and circumference of Earth to be?.

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  1. The Montauk Point Lighthouse on LongIsland has dual beams(two light sources opposite each other.) Ships at sea observe a blinking light every 5 seconds. What rotation speed is required todo this?

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  1. A race car is driven around a circular track at a constant speed of 180 mph. If the diameter of the track is ½ mile, what is the angular speed of the track in revolutions per hour ? ( = laps per hour).

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  1. A neighborhood has a merry-go-round whose radius is 25 feet. If the time for one revolution is 30 seconds, how fast is the merry-go-round going?

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