Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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HELP PLS. I have no idea how to do this. I need to do page 196 and 197 using data from page 200. Can you please write it down and explain so I can understand
14 of 128 High Dive: The Height and the Sine 199 Activity A Clear View As you may remember, the Ferris wheel at the amusement park where Al and Betty like to ride has a radius of 15 feet, and its center is 20 feet above ground level. This is not the same Ferris wheel as the one at the circus. The park's Ferris wheel turns with a constant angular speed. It takes 24 seconds for a complete turn. The fence around the amusement park is 13 feet high. Once Al and Betty get above the fence, there is a wonderful view. 1. During one revolution, what percentage of the time are Al and Betty above the height of the fence? 2. How would your answer to Question 1 change if the period were other than 24 seconds? 200 INTERACTIVE MATHEMATICS PROGRAM Extending the Sine Reference If the Ferris wheel at the circus turns counterclockwise at a constant angular speed of 9 degrees per second and the platform passes the 3o'clock position at t = 0, then the platform will remain in the first quadrant through t= 10. During this time interval, the platform's height above the ground is given by the formula
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Transcribed Image Text:14 of 128 High Dive: The Height and the Sine 199 Activity A Clear View As you may remember, the Ferris wheel at the amusement park where Al and Betty like to ride has a radius of 15 feet, and its center is 20 feet above ground level. This is not the same Ferris wheel as the one at the circus. The park's Ferris wheel turns with a constant angular speed. It takes 24 seconds for a complete turn. The fence around the amusement park is 13 feet high. Once Al and Betty get above the fence, there is a wonderful view. 1. During one revolution, what percentage of the time are Al and Betty above the height of the fence? 2. How would your answer to Question 1 change if the period were other than 24 seconds? 200 INTERACTIVE MATHEMATICS PROGRAM Extending the Sine Reference If the Ferris wheel at the circus turns counterclockwise at a constant angular speed of 9 degrees per second and the platform passes the 3o'clock position at t = 0, then the platform will remain in the first quadrant through t= 10. During this time interval, the platform's height above the ground is given by the formula
High Dive: Going to the Circus 195 Activity As the Ferris Wheel Turns To understand what happens when a diver is released from a moving Ferris wheel, you need precise information about the position of the diving platform as the Ferris wheel turns. In this activity, you will look only at the height of the platform. Later, you will consider how far the platform is to the left or right of the center of the wheel. You will need this information about the Ferris wheel. Use these facts throughout the unit, unless a problem specifically gives different information. Reminder: The circumference of a circle can be found from its radius using the formula C= 2mr. 1. At what speed is the platform moving (in feet per second) as it goes around on the Ferris wheel? 2. The rate at which an object turns is called angular speed, because it measures how fast an angle is changing. Angular speed does not depend on the radius. Through what angle (in degrees) does the Ferris wheel turn each second? continued i 196 INTERACTIVE MATHEMATICS PROGRAM 3. How many seconds does it take for the platform to go each of these distances? a. From the 3 o'clock to the 11 o'clock position b. From the 3 o'clock to the 7 o'clock position e. From the 3 o'clock to the 4 o'clock position 4. What is the platform's height off the ground at each of these times? a. 1 second after passing the 3 o'clock position b. 6 seconds after passing the 3 o'clock position c. 10 seconds after passing the 3o'clock position d. 14 seconds after passing the 3 o'clock position e. 23 seconds after passing the 3 o'clock position f. 49 seconds after passing the 3 o'clock position
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Transcribed Image Text:High Dive: Going to the Circus 195 Activity As the Ferris Wheel Turns To understand what happens when a diver is released from a moving Ferris wheel, you need precise information about the position of the diving platform as the Ferris wheel turns. In this activity, you will look only at the height of the platform. Later, you will consider how far the platform is to the left or right of the center of the wheel. You will need this information about the Ferris wheel. Use these facts throughout the unit, unless a problem specifically gives different information. Reminder: The circumference of a circle can be found from its radius using the formula C= 2mr. 1. At what speed is the platform moving (in feet per second) as it goes around on the Ferris wheel? 2. The rate at which an object turns is called angular speed, because it measures how fast an angle is changing. Angular speed does not depend on the radius. Through what angle (in degrees) does the Ferris wheel turn each second? continued i 196 INTERACTIVE MATHEMATICS PROGRAM 3. How many seconds does it take for the platform to go each of these distances? a. From the 3 o'clock to the 11 o'clock position b. From the 3 o'clock to the 7 o'clock position e. From the 3 o'clock to the 4 o'clock position 4. What is the platform's height off the ground at each of these times? a. 1 second after passing the 3 o'clock position b. 6 seconds after passing the 3 o'clock position c. 10 seconds after passing the 3o'clock position d. 14 seconds after passing the 3 o'clock position e. 23 seconds after passing the 3 o'clock position f. 49 seconds after passing the 3 o'clock position
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