Answer:
0.20 seconds
Step-by-step explanation:
Given the function:
For the distance traveled by a pendulum in time [tex]t[/tex]:
[tex]P(t)=-5cos(2\pi t)+5[/tex]
Where [tex]t[/tex] is in radians.
Also, given that [tex]P(t)=3.5\ cm[/tex]
To find:
The time [tex]t[/tex] = ? to the nearest hundredth.
Solution:
Putting the values as per given statements, it can be observed that:
[tex]3.5=-5cos(2\pi t)+5\\\Rightarrow -1.5=-5cos(2\pi t)\\\Rightarrow 0.3=cos(2\pi t)[/tex]
Taking the inverse:
[tex]cos^{-1}(0.3) = 2\pi t[/tex]
[tex]\Rightarrow 2\pi t=72.54^\circ[/tex]
We know that [tex]2\pi\ radians = 360^\circ[/tex]
Putting the value above:
[tex]\Rightarrow 360t=72.54^\circ\\\Rightarrow t = \dfrac{72.54}{360}\\\Rightarrow t =\bold{0.20}\ seconds[/tex]
So, after 0.20 seconds, the pendulum reaches 3.5 cm from the place it was released.
