4:43 or a quarter to 5
So there is 20 meters radius
If it takes 7 minutes to make a complete circle.
51.42857143 degrees a minute
t=0
Exactly 20 feet above the ground.
t = 7/4
40 feet above the ground
7/4 * 360/7 = 360/4 = 90 degrees
t = 14/4
9 o'clock position which is exactly 20 feet above the ground
t = 0. when t = 14/4, you are at exactly 14/4 * 360/7 = 180 degrees.
t = 21/4
Being 270 degrees
t = 28/4, you are back at the 3 o'clock position
28/4 equals 7 minutes because 7*4 = 28.
9 o'clock and 3 o'clock position
12 o'clock and 6 o'clock position
360/7 * t which is in minutes
20 plus the radius of the ferris wheel * the sin of the angle.
h = f(t) = 20 * (1 + sin(x)) where
x = 360/7 * t
t = minutes
h = the height you will be at.
when t = 0 which is 0 minutes, then:
x = 360/7 * t = 360/7 * 0 = 0 degrees
h = f(t) = 20 * (1 + sin(x)) becomes:
h = f(0) = 20 * (1 + sin(0))
since sin(0) = 0, this becomes:
h = f(t) = 20 * (1 + 0) = 20 * 1 = 20
you are 20 feet above the ground and you are at the 3 o'clock position
t = 7/4 which is 1.75 minutes
x = 360/7 * t = 360/7 * 7/4 = 360/4 = 90 degrees
h = f(t) = 20 * (1 + sin(t)) becomes
h = f(7/4) = 20 * (1 + sin(90))
since sin(90) = 1, this becomes:
h = f(7/4) = 20 * (1 + 1) = 20 * 2 = 40
you are 40 feet above the ground and you are at the 12 o'clock position
t = 14/4 which is 3.5 minutes, then:
x = 360/7 * t = 360/7 * 14/4 = 360*2/4 = 720/4 = 180 degrees
h = f(t) = 20 * (1 + sin(t)) becomes
h = f(14/4) = 20 * (1 + sin(180))
since sin(180) = 0, this becomes:
h = f(14/4) = 20 * (1 + 0) = 20 * 1 = 20
you are 20 feet above the ground and you are at the 9 o'clock position
when t = 21/4 which is 5.25 minutes, then:
x = 360/7 * t = 360/7 * 21/4 = 360*3/4 = 1080/4 = 270 degrees
h = f(t) = 20 * (1 + sin(t)) becomes
h = f(21/4) = 20 * (1 + sin(270))
since sin(270) = -1, this becomes:
h = f(14/4) = 20 * (1 - 1) = 20 * 0 = 0
you are 0 feet above the ground and you are at the 6 o'clock position of the ferris wheel which is at the bottom at ground level.
when t = 6 minutes, then:
x = 360/7 * 6 = 2160/7 = 308.5714286 degrees
h = f(t) = 20 * (1 + sin(t)) becomes
h = f(6) = 20 * (1 + sin(308.5714286))
since sin(308.5714286) = -.781831482, this becomes:
h = f(6) = 20 * (1 - .781831482) = 20 * .218168518 = 4.36337351
you are 4.36337351 feet above the ground and you are somewhere between the 4 o'clock and 5 o'clock position on the ferris wheel, much closer to the 5 o'clock position than the 4 o'clock position.
This would be roughly 4:43 or a quarter to 5. we are talking about the hour hand position.
