We need to solve the following expression:
[tex]h=-30\cdot\cos (\frac{2\pi}{5}\cdot t)[/tex]
For when h is equal to 20.
[tex]\begin{gathered} 20=-30\cdot\cos (\frac{2\pi}{5}t) \\ \cos (\frac{2\pi}{5}t)=-\frac{2}{3} \\ \arccos (\cos (\frac{2\pi}{5}t))=\arccos (-\frac{2}{3}) \\ \frac{2\pi}{5}t-2\pi\cdot n=\pm2.3 \\ \frac{2\pi}{5}t=\pm2.3+2\pi\cdot n \\ t=\pm\frac{11.5}{2\pi}+5n \\ \text{ For n =0.} \\ t=1.83 \\ \text{For n =1} \\ t=6.83\text{ and }t=3.17 \end{gathered}[/tex]
The answers are 1.8 seconds and 3.2 seconds.
