Answer:
\(t=\dfrac{3}{\pi}\left(\cos ^{-1}\dfrac{h}{7}\right)\)
Step-by-step explanation:
The given function is,
\(h=7\cos \left(\dfrac{\pi}{3}t\right)\)
\(\Rightarrow \cos \left(\dfrac{\pi}{3}t\right)=\dfrac{h}{7}\)
\(\Rightarrow \dfrac{\pi}{3}t=\cos ^{-1}\dfrac{h}{7}\)
\(\Rightarrow t=\dfrac{3}{\pi}\left(\cos ^{-1}\dfrac{h}{7}\right)\)
This is the solution of t.
Now we have to find t when h is 1 cm, 3 cm and 5 cm.
When h=1
\(t=\dfrac{3}{\pi}\left(\cos ^{-1}\dfrac{1}{7}\right)=78.10\ s\)
When h=3
\(t=\dfrac{3}{\pi}\left(\cos ^{-1}\dfrac{3}{7}\right)=61.71\ s\)
When h=5
\(t=\dfrac{3}{\pi}\left(\cos ^{-1}\dfrac{5}{7}\right)=42.41\ s\)
