The hands of a clock rotates through the same point over the same
periods of time, which is known as periodic motion.
Response:
- The equation that correctly describes the height of the fly as a function of time correctly is [tex]\underline{f(t) = 0.5 \cdot sin \left(\dfrac{\pi}{30} \cdot t - \dfrac{\pi}{3} \right) + 5.5}[/tex]
What type of equation describes the height of the fly?
The highest point of the tip = 6 feet above the ground
The lowest point of the tip = 5 feet above the ground
Time at which the fly lands on the second hand = 15 seconds after 10:10 pm
Required:
To write an equation that describes the height of the fly
Solution:
The general form of the equation for the sinusoidal (periodic or
repetitive) motion of is, given as follows;
f(t) = A·sin(B·t + C) + D
Where;
[tex]A = \dfrac{6 \, feet - 5 \, feet}{2} = \mathbf{0.5 \, feet}[/tex]
[tex]T = \mathbf{ \dfrac{2 \cdot \pi}{B}}[/tex]
Where;
T = The period = 60 seconds
Which gives;
[tex]B = \dfrac{2 \cdot \pi}{60} = \mathbf{\dfrac{ \pi}{30}}[/tex]
C = The horizontal shift
At t = 0, the location of the second hand is at 10 + 15 = 25 seconds after 12 (10 seconds after 10:15)
[tex]Angle \ of \ rotation \ below \ horizontal \ axis = \mathbf{\dfrac{10}{60} \times 2 \cdot \pi} = \dfrac{1}{3} \cdot \pi[/tex]
Which gives;
[tex]C= -\dfrac{1}{3} \cdot \pi[/tex]
[tex]The \ vertical \ shift, \ D = \mathbf{ \dfrac{6 \, feet + 5 \, feet}{2} }= 5.5 \, feet[/tex]
Which gives;
[tex]The \ height \ is \ correctly \ describes \ by \ \underline{f(t) = 0.5 \cdot sin \left(\dfrac{\pi}{30} \cdot t - \dfrac{\pi}{3} \right) + 5.5}[/tex]
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