A child is swinging a swing. Minimum and maximum heights fo swing from the earth's surface are 0.75 m and 2 m respectively. The maximum velocity of this swing is

Options

A. `5m//s`
B. `10m//s`
C. `15m//s`
D. `20m//s`

Answer

To find the maximum velocity of the swing, we can use the principle of conservation of energy. The potential energy at the maximum height will be converted into kinetic energy at the lowest point of the swing.

### Step-by-step Solution:

1. **Identify the heights**:
- Minimum height (h1) = 0.75 m
- Maximum height (h2) = 2 m

2. **Calculate the height difference (h)**:
- The height difference (h) that the swing descends is given by:
\[ h = h2 - h1 = 2 \, \text{m} - 0.75 \, \text{m} = 1.25 \, \text{m} \]

3. **Use the formula for maximum velocity**:
- The maximum velocity (V) at the lowest point can be calculated using the formula:
\[ V = \sqrt{2gh} \]
- Where \( g \) (acceleration due to gravity) is approximately \( 10 \, \text{m/s}^2 \).

4. **Substitute the values into the formula**:
- Substitute \( g = 10 \, \text{m/s}^2 \) and \( h = 1.25 \, \text{m} \):
\[ V = \sqrt{2 \times 10 \, \text{m/s}^2 \times 1.25 \, \text{m}} = \sqrt{25} = 5 \, \text{m/s} \]

5. **Conclusion**:
- The maximum velocity of the swing is \( 5 \, \text{m/s} \).

### Final Answer:
The maximum velocity of the swing is **5 m/s**.