1. **Problem statement:** A ball hangs from a string and swings from point B (bottom) to point A, which is 1.0 m above B. We want to find the minimum speed at point B so the ball just reaches point A. 2. **Relevant physics principle:** We use conservation of mechanical energy. The total mechanical energy (kinetic + potential) at point B must be enough to reach point A. 3. **Define variables:** - Height difference $h = 1.0$ m - Speed at bottom $v_B$ (unknown) - Speed at top $v_A = 0$ m/s (minimum speed to just reach A) 4. **Energy at point B:** $$E_B = K_B + U_B = \frac{1}{2}mv_B^2 + 0$$ (Potential energy zero at bottom) 5. **Energy at point A:** $$E_A = K_A + U_A = 0 + mg h$$ (Speed zero at top, potential energy $mg h$) 6. **Conservation of energy:** $$E_B = E_A$$ $$\frac{1}{2}mv_B^2 = mg h$$ 7. **Solve for $v_B$:** Cancel $m$ from both sides: $$\frac{1}{2}\cancel{m}v_B^2 = g h \cancel{m}$$ $$\Rightarrow v_B^2 = 2 g h$$ $$\Rightarrow v_B = \sqrt{2 g h}$$ 8. **Calculate numerical value:** Using $g = 9.8$ m/s$^2$ and $h = 1.0$ m: $$v_B = \sqrt{2 \times 9.8 \times 1.0} = \sqrt{19.6} \approx 4.43 \text{ m/s}$$ 9. **Answer:** The minimum speed at point B is approximately **4.4 m/s**, which corresponds to option C.