Asked by Shreya
Modelling with sine/cosine
A Ferris wheel has a diameter of 30m. The bottom of the wheel is 1.5m off the ground it takes 3.5min to make one complete revolution. a person gets on ferris wheel at its lowest point at time = 0.
write an equation that represents persons height above ground h at any time t
is the height 31.5? i added 30 to 1.5
how high off the ground is the person at t = 25s?
I don't get how to solve.
How long (in one rotation) is the person above 27m?
A Ferris wheel has a diameter of 30m. The bottom of the wheel is 1.5m off the ground it takes 3.5min to make one complete revolution. a person gets on ferris wheel at its lowest point at time = 0.
write an equation that represents persons height above ground h at any time t
is the height 31.5? i added 30 to 1.5
how high off the ground is the person at t = 25s?
I don't get how to solve.
How long (in one rotation) is the person above 27m?
Answers
Answered by
Reiny
Last post for tonight, going to bed
diameter is 30 m, so a=15
So, (recall the last question with the 18 and 19)
the min value is going to be -15 , but we want it to be 1.5 above ground , (the x-axis)
so we have to add 16.5
sofar we have
y = 15 sin k(t + d) + 16.5 , t in minutes
it takes 3.5 minutes for one rotation
period = 3.5
but 2π/k = 3.5
3.5k = 2π
k = 2π/3.5 or 4π/7
getting there ....
y = 15 sin (4π/7)(t + d) + 16.5
when t= 0 , we have the lowest point ---> (0,1.5)
1.5 = 15 sin (4π/7)(0+d) + 16.5
-1 = sin ((4π/7)(d) )
I know sin 3π/2 = -1
so (4π/7)d = (3π/2)
d = 21/8
ok, how about
<b>y = 15 sin (4π/7)(t + 21/8) + 16.5</b>
testing:
if t=3.5, we should get 31.5
y = 15sin(4π/7)(3.5 - 21/8) + 16.5
= 15 sin (π/2) + 16.5 = 15(1) + 16.5 = 31.5 , Wow!!
-------------------------------
when t=25 seconds = 25/60 min or 5/12 min
y = 15sin (4π/7)(5/12 + 21/8) + 16.5
= 15 sin( 73π/42) + 16.5
= 5.5 m high
----------------------
Here comes the hard part:
we want y to be above 27
sketch a line y = 27 to cut our cosine curve, you will see two such places in each period
Let's find those two values of t
27 = 15sin(4π/7)(t+21/8) + 16.5
sin(4π/7)(t+21/8) = .7
set your calculator to radians and do inverse sin (.7)
I get .7754
but by the Cast rule, we know the sine is positive in quadrants I and II
so (4π/7)(t+21/8) = .7754 OR (4π/7)(t+21/8) = π - .7754
t+21/8 = .43193 OR t+21/8 = 2.366
t = -2.193 or t = -.2588
don't worry about the t values being negative, the show we are on the left part of the cosine curve. We could add 3.5 to both to make them positive
So the time interval = -.2588 - (-2.193) = 1.934 minutes or 116 seconds
diameter is 30 m, so a=15
So, (recall the last question with the 18 and 19)
the min value is going to be -15 , but we want it to be 1.5 above ground , (the x-axis)
so we have to add 16.5
sofar we have
y = 15 sin k(t + d) + 16.5 , t in minutes
it takes 3.5 minutes for one rotation
period = 3.5
but 2π/k = 3.5
3.5k = 2π
k = 2π/3.5 or 4π/7
getting there ....
y = 15 sin (4π/7)(t + d) + 16.5
when t= 0 , we have the lowest point ---> (0,1.5)
1.5 = 15 sin (4π/7)(0+d) + 16.5
-1 = sin ((4π/7)(d) )
I know sin 3π/2 = -1
so (4π/7)d = (3π/2)
d = 21/8
ok, how about
<b>y = 15 sin (4π/7)(t + 21/8) + 16.5</b>
testing:
if t=3.5, we should get 31.5
y = 15sin(4π/7)(3.5 - 21/8) + 16.5
= 15 sin (π/2) + 16.5 = 15(1) + 16.5 = 31.5 , Wow!!
-------------------------------
when t=25 seconds = 25/60 min or 5/12 min
y = 15sin (4π/7)(5/12 + 21/8) + 16.5
= 15 sin( 73π/42) + 16.5
= 5.5 m high
----------------------
Here comes the hard part:
we want y to be above 27
sketch a line y = 27 to cut our cosine curve, you will see two such places in each period
Let's find those two values of t
27 = 15sin(4π/7)(t+21/8) + 16.5
sin(4π/7)(t+21/8) = .7
set your calculator to radians and do inverse sin (.7)
I get .7754
but by the Cast rule, we know the sine is positive in quadrants I and II
so (4π/7)(t+21/8) = .7754 OR (4π/7)(t+21/8) = π - .7754
t+21/8 = .43193 OR t+21/8 = 2.366
t = -2.193 or t = -.2588
don't worry about the t values being negative, the show we are on the left part of the cosine curve. We could add 3.5 to both to make them positive
So the time interval = -.2588 - (-2.193) = 1.934 minutes or 116 seconds
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.