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Hammer Speed Cd5480

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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:** $$\boxed{8.40 \text{ m/s}}$$