1. **State the problem:** We need to find the height of Martz (chair M) above the ground at time $t=9$ minutes. 2. **Given information:** - Diameter of Ferris wheel = 50 meters, so radius $r = \frac{50}{2} = 25$ meters. - Lowest point is 3 meters above the ground. - Center height $= 3 + 25 = 28$ meters. - The wheel completes one full revolution every 12 minutes. - Chair M starts at the lowest point at $t=0$. 3. **Formula for height of a point on a Ferris wheel:** $$h(t) = \text{center height} + r \sin(\theta(t))$$ where $\theta(t)$ is the angle in radians the chair has rotated from the starting position. 4. **Calculate angular velocity:** One full revolution $= 2\pi$ radians in 12 minutes, so $$\omega = \frac{2\pi}{12} = \frac{\pi}{6} \text{ radians per minute}$$ 5. **Calculate angle at $t=9$ minutes:** $$\theta(9) = \omega \times 9 = \frac{\pi}{6} \times 9 = \frac{9\pi}{6} = \frac{3\pi}{2}$$ 6. **Calculate height at $t=9$:** $$h(9) = 28 + 25 \sin\left(\frac{3\pi}{2}\right)$$ Since $\sin\left(\frac{3\pi}{2}\right) = -1$, $$h(9) = 28 + 25 \times (-1) = 28 - 25 = 3$$ 7. **Interpretation:** At $t=9$ minutes, chair M is at the lowest point again, 3 meters above the ground. **Final answer:** $$\boxed{3 \text{ meters}}$$