A 3.0 kg rock sits on a 0.80 meter ledge. If it is pushed off, how fast will it be going at the

bottom?

To find the speed of the 3.0 kg rock when it reaches the bottom, we can use the concept of energy conservation. Since the rock is initially at rest, its potential energy at the top will convert into kinetic energy at the bottom.

### Steps:
1. **Potential Energy (PE) at the top:**
   \[
   PE = mgh
   \]
   where:
   - \( m \) is the mass of the rock (3.0 kg),
   - \( g \) is the acceleration due to gravity (9.8 m/s²),
   - \( h \) is the height of the ledge (0.80 m).

   \[
   PE = 3.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.80 \, \text{m}
   \]
   \[
   PE = 23.52 \, \text{J}
   \]

2. **Kinetic Energy (KE) at the bottom:**
   Since energy is conserved, all the potential energy will convert to kinetic energy:
   \[
   KE = \frac{1}{2} mv^2
   \]
   Set \( KE = PE \), so:
   \[
   \frac{1}{2} mv^2 = 23.52 \, \text{J}
   \]

3. **Solving for velocity (\(v\)):**
   \[
   v^2 = \frac{2 \times 23.52 \, \text{J}}{3.0 \, \text{kg}}
   \]
   \[
   v^2 = 15.68
   \]
   \[
   v = \sqrt{15.68} \approx 3.96 \, \text{m/s}
   \]

### Final Answer:
The rock will be going approximately **3.96 m/s** when it reaches the bottom.

Would you like further details on this solution?

Here are 5 related questions:
1. How would the speed change if the height of the ledge increased?
2. What would happen if the mass of the rock were doubled?
3. How would air resistance affect the rock's speed?
4. Can this method be applied to objects with different shapes or densities?
5. How can we calculate the time it takes for the rock to reach the ground?

**Tip:** Energy conservation principles are very useful for solving problems involving falling objects, especially when friction or air resistance is negligible.

A 3.0 kg rock sits on a 0.80 meter ledge. If it is pushed off, how fast will it be going at the bottom?

Learn how to calculate the speed of a 3.0 kg rock falling from a 0.80-meter ledge using energy conservation. This problem covers key physics concepts such as potential energy, kinetic energy, and the law of conservation of energy. Suitable for students in Grades 9-12.

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