You are on a ferris wheel. The diameter of the ferris wheel is 36 feet and the center of the ferris wheel is 20 feet above the ground. The ferris wheel rotates counter clockwise.
1. How high off the ground are you when you are at the top of the ferris wheel?
2. How high off the ground are you when you have rotated 30 degrees past horizontal.
I WANT TO SEE LOTS O' MATH FOR #2!
For the first question, I got that you would be about 44 feet (√1924) above the ground when you're at the top of the ferris wheel.
ReplyDeleteFor the second question I'm having trouble; hopefully someone comes along and explains how to solve it.
Anyways..
I solved the first question by doing what we've been learning in class. Because the diameter of the ferris wheel is 36ft, half of that, 18ft, would be the radius or the length of the adjacent side of the triangle. The height, or opposite side of the triangle would be 40 ft because the center of the ferris wheel is 20 ft above ground suggesting that the very top of the ferris wheel would be 40 ft above ground. Then I used the pythagorean theorem to solve for the hypotenuse, which rounded to 44 (√1924). So that would mean that when you're at the top of the ferris wheel you'll be about 44ft above the ground.
PLEASE EXPLAIN HOW TO DO QUESTION #2
For the first question i got 38 feet because the radius of the ferris wheel is 18 feet and the center of the ferris wheel is 20 feet off the ground so i added 20 to 18 and i got 38 for the answer. The second question it uses the unit circle meaning it went below the x axis and 30 degrees below 0 is 330 degrees which has the coordinates (√3/2) as the X and (-1/2) as the Y and I just plugged in 20 where the numbers are and i got (3.9) as the X and (-10) as the Y and i made a triangle like that and then used the Pythagorean theorem to find the hypotnuse which will be the arm length and i got 10.73 which i subtracted from 20 and got 9.27. Im sure this might be wrong but i don't know
ReplyDelete1) 54ft.
ReplyDeleteI did something similar to what Cynthia did and got a different answer. I know that the radius of the Ferris wheel is 18, I know this because it's half of the diameter, 36. After drawing a circle with a diameter(36), I drew a horizontal line through the middle of it. I then drew a triangle on one of the 4 sides of the triangle, and on the triangle, the height was 20ft and the base was 18ft. To get the hypotenuse,I used the Pythagorean theorem, and i got 26.90724809, rounded to 27. I multiplied 27 by 2(i multiplied by 2 to count the other half of the circle)and got 54ft.
I'm not sure if this is right though.
And as for #2, I have no idea how to even start it, I hope the next person is able to get the right answer.
1)38
ReplyDeletei 38 because the diameter all around the circle is 36 and the ferris wheel is 2 because it is 20 feet above the ground and the distance from the ground is 20 feet so 20-18=2 ft off the ground so 36+2=38 at the top.
i was not sure about 2 because i was not sure if we were supposed to us the Pythagorean using the radius 18 from the horizontal and the radius to the top in some way.
i have no idea how to do number 2, but the answer to number 1 is 38 because the diameter of the ferris wheel is 36 feet, and 36/2 is 18. the center is 20 feet off the ground, and 20+18 is 38.
ReplyDelete1) I believe the answer is 38. I added 18+20. because 36 is the diameter the radius is 18. the ferris wheel is 20 ft off the ground. so from the pavement to the center of the ferris wheel. from the center to the very top is 18. so i added 18+20 and got 38.
ReplyDeleteFor the second question, the answer is 9. I created a right triangle (30-60-90) and used the trigonomic ratios to find the height of the triangle.
ReplyDelete1. 38 because to find the height you need to do radius + the height off the ground it is. 18+20=38.
ReplyDelete2. Horizontal would be 180 degrees. On the unit circle when you rotate 30 degrees counter clockwise you are at 150 degrees where the y value is 1/2.
for 1) i got 38ft
ReplyDelete- okay this how i got 38ft, okay so the whole ferris wheel is 36 ft. so that means from the middle point of the ferris wheel/circle to the top of the circle is 18ft. also you know that the middle point to the ground is 20 ft. so to find out your height at the top of the circle you simply add 18ft + 20 ft = 38ft sand thats how high you are from the ground.
for 2) i got 32 ft
- the reason it is 32 ft is because if you were to put this on a coordinate plane and divide this into 4 parts of the coordinate plane, each quadrant would have 9ft because 36/4. so if u start at the top of the circle and go counter clockwiseu would get 9+9+9 then u would go up 3. the reason you would go up 3 is because you have to go 30 degress past horizontal and the 3 represents 30 degrees. so once u add 9+9+9+3 you get 30 and than you have to add 2 because the ferris wheel is still 20 feet off the ground.
-Taylor Jacobs, pd 6
Here are the facts that it gives you: the diameter is 36ft, the center of the circle is 20ft above the ground, and the wheel rotates to the left. From this we can determine that the radius is 18ft, 36/2=18.
ReplyDeleteSo that means that from the top to the center is 18, and we know that from the center to the ground is 20, then we know that 18+20=38.
*So for the first question, you are 38ft high when you are at the top of the ferris wheel.
The second question involves knowledge of the unit circle. You need to know that the coordinate of a 30degree angle in the first quadrant is (1/2,root 3 over 2). This means that you would be root 3 over 2 above the horizontal point.
This means that if you are 30 degrees past the horizontal, then you would be root 3 over 2 ft plus 20ft off the ground. The square root of 3 is 1.732050808, divide that by 2 an you get 0.866025404 Add 20 to this and you get 20.8660254
So for the second question, you would be 20.8660254
feet off the ground when you are 30 degrees past the horizontal.