1. **Problem:** A ball is dropped from the top of a building and strikes the ground with a speed of 30 m/s. We need to find the height of the building. 2. **Formula:** We use the kinematic equation for free fall without air resistance: $$v^2 = u^2 + 2gh$$ where: - $v$ is the final velocity (30 m/s), - $u$ is the initial velocity (0 m/s, since the ball is dropped), - $g$ is the acceleration due to gravity (approximately 9.8 m/s$^2$), - $h$ is the height of the building. 3. **Calculation:** Substitute the known values: $$30^2 = 0 + 2 \times 9.8 \times h$$ $$900 = 19.6h$$ Solve for $h$: $$h = \frac{900}{19.6} \approx 45.92$$ 4. **Interpretation:** The height of the building is approximately 46 meters, which is closest to option C (45 m). **Final answer:** C. 45 m