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Answer:
Step-by-step explanation:
We can find the sinusoidal function of the Ferris wheel with a radius of 20 m and completes 1 rotation every 30 seconds by using this formula:
[tex]\boxed{y=Asin(\omega t+\phi_0)+y_0}[/tex]
where:
Refer to the picture, we can find that the equilibrium position (y₀) is the total of Ferris wheel distance from ground and the radius, therefore:
[tex]y_0=2+20=22\ m[/tex]
From the picture, we can also find the amplitude (A) and the initial phase (φ₀):
"The Ferris wheel completes one rotation every 30 seconds" means the period (T) of the Ferris wheel equals to 30 s. We can find the angular velocity (ω) by using this formula:
[tex]\boxed{\omega=\frac{2\pi}{T} }[/tex]
[tex]\begin{aligned}\\\omega&=\frac{2\pi}{30} \\\\&=\frac{\pi}{15} \ rad/s\end{aligned}[/tex]
By putting in all the information, we can come up with the sinusoidal function:
[tex]\begin{aligned}y&=Asin(\omega t+\phi_0)+y_0\\\\y&=20\cdot sin\left(\frac{\pi}{15} t+\left(-\frac{\pi}{2} \right)\right)+22\\\\\bf y&\bf=20\cdot sin\left(\frac{\pi}{15} t-\frac{\pi}{2} \right)+22\end{aligned}[/tex]
To determine the height of the passenger after 7 seconds, we substitute t with 7:
[tex]\begin{aligned}y&=20\cdot sin\left(\frac{\pi}{15} t-\frac{\pi}{2} \right)+22\\\\&=20\cdot sin\left(\frac{\pi}{15} (7)-\frac{\pi}{2} \right)+22\\\\&=20\cdot sin\left(-\frac{\pi}{30} \right)+22\\\\&\approx\bf 21.94\ m\end{aligned}[/tex]
