Apps. and Interpretation for IBDP Maths Ebook 1 | Page 153

3. The height of a seat on a Ferris wheel in metres is modelled by the function
h( t) � �pcos( qt)
� r , where p , q and r are positive, and t is the number of minutes
after 9:00.
12
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]
(i) p ;
(ii) q ;
(c)
(iii) r .
Find the time for the seat to be 60 metres above the ground for the fifth time.
[6]
[4]
4. The height of a seat on a Ferris wheel in metres is modelled by the function
h( t) � �pcos( qt)
� r , where p , q and r are positive, and t is the number of minutes
after 12:45.
The seat starts at the lowest point and its height is 3 metres above the ground. The
diameter of the wheel is 70 metres and the first time the seat is 73 metres above the
ground is 12:58.
(a)
Find the value of
(i) p ;
(ii) q ;
(iii) r .
(b) Find the height of the seat above the ground at 13:41.
(c) Find the time for the seat to be 10 metres above the ground for the sixth time.
[7]
[2]
[4]
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