00:01
Alright, so we have a ferris wheel has a 42 -foot radius in the center of the ferris wheels at 50 feet above the ground.
00:14
The ferris wheel rotates in a counterclockwise direction at a constant angular speed of three radiance per minute.
00:23
Antonio boards the ferris wheel at the 3 o 'clock position and rides the ferris wheel for many rotations.
00:31
Let t represent the number of minutes since the ride started.
00:34
First thing is write an expression in terms of t to represent the number of radiance antonio swept out from the 3 o 'clock position since the ride has started.
00:49
So because he is going at 3 radiance per mission per minute, then you would have 3.
01:15
Three and that would get you the answer for after two minutes he would go six ratings almost completely all the way around but not quite second question so there's your expression 3t and see how do they want you yeah expression in terms of t that would be it how long did it take for antonio to complete one revolution all that then is 3 t as to equal to pi.
01:47
Well, here's all the t would divide by three.
01:51
So it takes 2 pi divided by 3 to get all the way around, or 2 .094 -395, 1, 239 seconds, or minutes.
02:06
So 2 minutes and 0 .09 of a minute.
02:13
That's b.
02:14
C then says, what theta be the angle in terms of antonial, in radiance, antonia, is rotated counterclockwise from the 3 o 'clock position.
02:25
Write a function h that determines antonio's height above the ground in terms of theta.
02:34
So if you're rotating theta and you want to figure out the height above the ground, well, that would be the distance from the x -axis up to wherever, and if they're rotating around a circle, then to find that height, that's the y value of the circle part so you're going to have to have because it shifted up 50 plus and then the y value of the circle so the circle has a radius of 42 times and the y value is sign of theta and that would get you the height because when theta is between 0 and 180 degrees, sign is positive, and that means it's above the 50 to 50 footmark.
03:40
And when theta is between 180 and 360, then it's below the 50 foot mark, and the sign is a negative number.
03:48
So you'd be subtracting an amount.
03:51
And like at 90 degrees, that's straight up.
03:55
So the sign of 90 degree angle is 1, so that's straight up 42.
03:59
And 50 plus 42 would be 92.
04:03
And when you go straight down, that would be 270 degrees or 3 pi over 2.
04:09
And sign at that point is a negative 1, and 42 times a negative 1 is a negative 42, and 50 plus a negative 42 is 8.
04:18
And so that would be your equation to figure out the height above the ground.
04:26
Now then, the next question says the height above ground in terms of theta.
04:36
Oh, we just did that...