Analysis and Approaches for IBDP Maths Ebook 1 | Page 111

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2. The height of the water in metres is modelled by the function h( t) � pcos( qt)
� r , where
t is the number of hours after 12 hours on 23 August 2018, for 0 �t
� 72 .
The point A (6.5, 4.2) represents the first high tide and B (13,1.8) represents the next low
tide.
(a) (i) How much time is there between the first high tide and the next high
tide?
(b)
(c)
(ii) Find the difference in height between low tide and high tide.
Find the value of
(i) p ;
(ii) q ;
(iii) r .
Find the time when the second low tide on 25 August 2018 occur.
[4]
[6]
[3]
3. The height of a seat on a Ferris wheel in metres is modelled by the function
h( t) � pcos( qt)
� r , where t is the number of minutes after 9:00.
The seat starts at the lowest point and its height is one metre above the ground. The
radius of the wheel is 45 metres and the first time the seat is 46 metres above the ground
is 9:09.
(a)
(b)
Find the time for the seat to be 91 metres above the ground for the first time.
Find the value of
[2]
10
(c)
(i) p ;
(ii) q ;
(iii) r .
Find the time for the seat to be 60 metres above the ground for the fifth time.
[6]
[4]
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