The motion of the hour hand of a clock is a periodic motion that repeats every 12 hours.
- The equation that can be used to models the height as a function of time, based on the given options, is presented as follows;
Reasons:
The given parameters are;
The variation of the height of the tip of the hour hand = 9 feet to 10 feet
At t = 0, the time = 12.00 a.m.
Required: The equation that can be used to model the height as a function of time.
Solution:
The general form of the cosine function is presented as follows;
y = a·cos(b·x - c) + d
The amplitude = a
Therefore;
b = The cycle speed
The period, T, is given as follows;
The period of a block, T = 12 hours
Therefore;
At t = 0, H = The highest point = 10 ft.
Which gives;
-c = arcos(1) = 0
-c = 0
c = 0
The equation is therefore;
The above equation is the same as; <u>H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5</u>
Learn more about the cosine function here: