This problem is similar to Problem 6 on your 7.5 worksheet. A Ferris wheel is 32
ID: 3122050 • Letter: T
Question
This problem is similar to Problem 6 on your 7.5 worksheet. A Ferris wheel is 32 meters in diameter and makes one revolution every 7 minutes. Suppose you board the Ferris wheel at the 6:00 position. For each of the questions below, round your answer to the nearest thousandth of a minute. (a) After how many minutes will you be 24 meters above the ground for the first time? minutes. (b) After how many (total) minutes will you be 24 meters above the ground for the second time? minutes. (c) For how many minutes of any revolution will your seat be 24 meters or more above the ground? minutes.Explanation / Answer
c)360 degrees in a circle. It makes 1 circle per 7 minutes. that is 360/7=51.4degrees a minute.
when the wheel is half way up you will be 16 feet off the ground. So draw a circle with a line through the center parallel to the ground. Ok move up the circle to the point where you would be 24 feet off the ground. Draw a line from that point to the center of the circle. Now all you need to do is find the angle of that arc.
To do that you can draw a line from the point at 24 feet mark perpendicular to the ground.until it crosses the first line you drew at the 16 foot mark. Now you have a right triangle.
The hypotenuse is 16 feet which is the radius of the wheel or circle.
the short leg would be 24-16 = 8feet.
the sine of an angle = the opposite over hypotenuse
8/16=1/2=0.5
inverse sine of .5=30 degrees.
so the wheel will be at or above 24 feet from 120 degrees to 240 degrees.
120=30 plus the 90 degrees to get to 24 feet.
240 degrees =270 which is once again where you reach 24 feet minus 30 degrees which is where you drop below 24 feet.
240-120 degrees divide this by the speed of 51.4 degrees/minute and you get 2.334 minutes it will be at or above 24 feet.
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