1. **State the problem:** We need to find the height of the paddle blade after 7 seconds based on the given piecewise graph description. 2. **Analyze the graph segments:** - From 0 to 2 seconds, the blade moves from 1 m above water to -1 m (enters water). - From 2 to 4 seconds, it rises back from -1 m to 1 m. - From 4 to 8 seconds, the blade oscillates sinusoidally between 0 m and 3 m with a period of about 2 seconds. 3. **Focus on the last segment (4 to 8 seconds):** - The oscillation has amplitude $A = \frac{3 - 0}{2} = 1.5$ m. - The midline (vertical shift) is $y = 1.5$ m (since it oscillates between 0 and 3). - The period $T = 2$ seconds. 4. **Write the sinusoidal function for height $h(t)$ for $t$ in $[4,8]$: ** $$h(t) = 1.5 + 1.5 \sin\left(\frac{2\pi}{2}(t - 4)\right) = 1.5 + 1.5 \sin(\pi (t - 4))$$ 5. **Calculate height at $t=7$ seconds:** $$h(7) = 1.5 + 1.5 \sin(\pi (7 - 4)) = 1.5 + 1.5 \sin(3\pi)$$ 6. **Evaluate $\sin(3\pi)$:** $$\sin(3\pi) = 0$$ 7. **Therefore:** $$h(7) = 1.5 + 1.5 \times 0 = 1.5$$ 8. **Interpretation:** The blade height at 7 seconds is 1.5 metres above the water surface. **Final answer:** The blade will be approximately 1.5 metres high after 7 seconds.