A body is dropped from a certain height to the ground. When it is halfway down, it possesses

Options

A. only kinetic energy
B. only potential energy
C. both kinetic energy and potential energy
D. neither kinetic energy nor potential en ergy

Answer

To solve the problem of a body dropped from a certain height and determining the types of energy it possesses when it is halfway down, we can break it down into steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- When the body is dropped from a height \( h \), its initial velocity \( v_0 = 0 \).
- At this point, the potential energy (PE) is maximum, and the kinetic energy (KE) is zero.
- The potential energy at the height \( h \) is given by the formula:
\[ PE = mgh \]
- Kinetic energy at this point is:
\[ KE = \frac{1}{2}mv_0^2 = 0 \]

2. **Analyzing the Body at Halfway Down**:
- When the body is halfway down, it has fallen to a height of \( \frac{h}{2} \).
- At this point, it will have some velocity \( v \) (which is not zero).
- The potential energy at this halfway point is:
\[ PE = mg\left(\frac{h}{2}\right) = \frac{mgh}{2} \]

3. **Calculating Kinetic Energy at Halfway**:
- To find the kinetic energy at this point, we can use the conservation of mechanical energy principle. The total mechanical energy at the top (initially) is equal to the total mechanical energy halfway down.
- Initial total energy (at height \( h \)):
\[ E_{initial} = PE + KE = mgh + 0 = mgh \]
- Total energy halfway down:
\[ E_{halfway} = PE + KE = \frac{mgh}{2} + KE \]
- Setting these equal (conservation of energy):
\[ mgh = \frac{mgh}{2} + KE \]
- Rearranging gives:
\[ KE = mgh - \frac{mgh}{2} = \frac{mgh}{2} \]

4. **Final Energy Calculation**:
- Thus, at halfway down, the kinetic energy is:
\[ KE = \frac{mgh}{2} \]
- Therefore, at halfway down, the body possesses both potential energy and kinetic energy:
- Potential Energy: \( \frac{mgh}{2} \)
- Kinetic Energy: \( \frac{mgh}{2} \)

5. **Conclusion**:
- The body possesses both kinetic energy and potential energy when it is halfway down.

### Final Answer:
The correct option is **3: both kinetic energy and potential energy**.