Hammer Speed Cd5480
1. **State the problem:** A hammer of mass 2.30 kg falls from the top of a 4.60 m high scaffold. We need to find the hammer's speed when it is 1 meter above the ground.
2. **Identify known values:**
- Initial height, $h_i = 4.60$ m
- Final height, $h_f = 1.00$ m
- Mass, $m = 2.30$ kg (mass will cancel out in this problem)
- Acceleration due to gravity, $g = 9.8$ m/s$^2$
3. **Relevant formula:** Use conservation of energy or kinematic equations. Here, we use the kinematic equation for velocity under constant acceleration:
$$v = \sqrt{2g\Delta h}$$
where $\Delta h$ is the vertical distance fallen.
4. **Calculate the distance fallen:**
$$\Delta h = h_i - h_f = 4.60 - 1.00 = 3.60 \text{ m}$$
5. **Calculate the speed:**
$$v = \sqrt{2 \times 9.8 \times 3.60} = \sqrt{70.56} \approx 8.40 \text{ m/s}$$
6. **Interpretation:** The hammer's speed when it is 1 meter from the ground is approximately 8.40 m/s downward.
**Final answer:**
$$\boxed{8.40 \text{ m/s}}$$