1. **State the problem:** A kid uses a pulley with 78.0% efficiency to lift 7.5 kg of materials using 265 J of energy. We need to find the height the materials are lifted. 2. **Formula and concepts:** Efficiency ($\eta$) is the ratio of useful work output to work input: $$\eta = \frac{\text{useful work output}}{\text{work input}}$$ Useful work output here is the gravitational potential energy gained by the materials: $$W_{out} = mgh$$ where $m$ is mass, $g$ is acceleration due to gravity (9.8 m/s$^2$), and $h$ is height. 3. **Calculate useful work output:** $$W_{out} = \eta \times W_{in} = 0.78 \times 265 = 206.7 \text{ J}$$ 4. **Use the potential energy formula to find height:** $$W_{out} = mgh \Rightarrow h = \frac{W_{out}}{mg}$$ 5. **Substitute values:** $$h = \frac{206.7}{7.5 \times 9.8}$$ 6. **Simplify denominator:** $$7.5 \times 9.8 = 73.5$$ 7. **Calculate height:** $$h = \frac{206.7}{73.5} \approx 2.81 \text{ meters}$$ 8. **Consider significant figures:** Given data has 3 significant figures, so final answer is: $$\boxed{2.81 \text{ meters}}$$