On a particular day the height, h metres, of the tide at Weymouth, relative to a certain point, can be modelled by the equation h = 5 sin(30t)o where t is the time in hours after midnight. a. Sketch the graph h against t for 0 ≤ t ≤ 12. b. Estimate the height of the tide, relative to the same point, at 2 pm that day.
Answers
Answer:
5.2 ans is correct my self
hope it helps
Answer:
The height, h, in metres of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function
h
(
t
)
=
5
sin
(
30
(
t
−
5
)
)
+
7
At the time of high tide
h
(
t
)
will be maximum when
sin
(
30
(
t
−
5
)
)
is maximum
This means
sin
(
30
(
t
−
5
)
)
=
1
⇒
30
(
t
−
5
)
=
90
⇒
t
=
8
So first high tide after midnight will be at
8
am
Again for next high tide
30
(
t
−
5
)
=
450
⇒
t
=
20
This means second high tide will be at
8
pm
So at 12 hr interval the high tide will come.
At the time of low tide
h
(
t
)
will be minimum when
sin
(
30
(
t
−
5
)
)
is minimum
This means
sin
(
30
(
t
−
5
)
)
=
−
1
⇒
30
(
t
−
5
)
=
−
90
⇒
t
=
2
So first low tide after midnight will be at
2
am
Again for next low tide
30
(
t
−
5
)
=
270
⇒
t
=
14
This means second low tide will be at
2
pm
So after 12 hr interval the low tide will come.
Here period is
2
π
ω
=
360
30
h
r
=
12
h
r
so this will be interval between two consecutive high tide or between two consecutive low tide