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secondary 4 | A Maths
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I am unsure as to why the answer key says, for (i), that coskt=-1 is where the maximum height occurs, which is 160m.
Date Posted: 3 years ago
Views: 195
you probably know that -1 ≤ cos x ≤ 1
Likewise,
-1 ≤ cos kt ≤ 1
Now the height of the capsule h is given as
80(1 - cos kt)
The height of the flyer itself is basically the same as the highest point a capsule can go to.
That means you want the biggest value of h.
Since h = 80(1 - cos kt), we want the smallest value of cos kt to make h the biggest possible.
Smallest value cos kt = -1.
So biggest h = 80(1 - (-1))
= 80(1 + 1)
= 80(2)
= 160
Likewise,
-1 ≤ cos kt ≤ 1
Now the height of the capsule h is given as
80(1 - cos kt)
The height of the flyer itself is basically the same as the highest point a capsule can go to.
That means you want the biggest value of h.
Since h = 80(1 - cos kt), we want the smallest value of cos kt to make h the biggest possible.
Smallest value cos kt = -1.
So biggest h = 80(1 - (-1))
= 80(1 + 1)
= 80(2)
= 160
Because the equation involves subtracting cos kt, we want a negative value for cos kt such that subtracting a negative becomes addition, so that we get the biggest h
Actually it's much easier to say that the height of the Singapore Flyer is twice the amplitude.
The height of the Singapore flyer is two amplitudes long regardless of the position of the base of the Flyer.
The height of the Singapore flyer is two amplitudes long regardless of the position of the base of the Flyer.
Weirdly enough the diameter of the wheel is only 150 m and the highest point is 165 m from the ground based on the statistics itself.
Weird that "ground level" does not really look like ground level from the picture; it's more of "a few metres" above ground level.
The height of the flyer isn't the same as the diameter of the wheel. You do realise the Flyer is about 3 storeys above ground ?
Oh... thank you guys for the help, I managed to solve the other parts but I couldn’t explain (i). But thank you both for your input :-)
'The height of the flyer is twice the amplitude' only holds for this question since the lowest point is taken to be 0m (ground level).
It does not take into account where the base of the Flyer really is. It also does not take into account the clearance height between the lowest point of the wheel and the ground where one steps onto the flyer from.
It does not take into account where the base of the Flyer really is. It also does not take into account the clearance height between the lowest point of the wheel and the ground where one steps onto the flyer from.
The equation modelling it seems to be wrong...
Actually all along I thought the base of the wheel is only 5 to 10 m above the ground
Actually all along I thought the base of the wheel is only 5 to 10 m above the ground
The boarding point is actually at level 3 if you've actually been there. The 3 storeys are higher than your typical 3 floors of a HDB flat
Besides, the equation is called a model for good reason. It doesn't actually represent the real thing exactly. Nothing wrong or right about it.
See 1 Answer
h = 80(1- cos kt)
Max of cos kt = 1. What happens to h?
Min of cos kt = -1. What happens to h?
(Hint: 1-(-1) = 1 + 1 = 2)
Max of cos kt = 1. What happens to h?
Min of cos kt = -1. What happens to h?
(Hint: 1-(-1) = 1 + 1 = 2)
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