The depth of water, w metres, in a particular harbour can be modelled by the function w(t) = a cos (bt) + d where t is the length of time, in minutes, after 06 : 00. On 20 January, the first high tide occurs at 06:00, at which time the depth of water is 18 m. The following low tide occurs at 12: 15 when the depth of water is 4m. This is shown in the diagram.
The depth of water, w metres, in a particular harbour can be modelled by the function w(t) = a cos (bt) + d where t is the length of time, in minutes, after 06 : 00. On 20 January, the first high tide occurs at 06:00, at which time the depth of water is 18 m. The following low tide occurs at 12: 15 when the depth of water is 4m. This is shown in the diagram.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a)
(b)
The depth of water, w metres, in a particular harbour can be modelled by the
function w(t) = a cos (btᵒ) + d where t is the length of time, in minutes,
after 06 : 00.
On 20 January, the first high tide occurs at 06: 00, at which time the depth of
water is 18 m. The following low tide occurs at 12:15 when the depth of
water is 4m. This is shown in the diagram.
(e)
(f)
20
16-
12
8-
4-
0
0
60
120
Find the value of a.
180
240
300
Find the value of d.
Find the period of the function in minutes.
Find the value of b.
360
420
18-4 = 14
(c)
(d)
Naomi is sailing to the harbour on the morning of 20 January. Boats can enter or
leave the harbour only when the depth of water is at least 6 m.
Find the latest time before 12:00, to the nearest minute, that
Naomi can enter the harbour.
480
Find the length of time (in minutes) between 06 : 00 and
15:00 on 20 January during which Naomi cannot enter or
leave the harbour.
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