A stone is dropped from the top of a tower. If it hits the ground after 10 seconds, what is the height of the tower?

Explanation

To find the height of the tower from which the stone is dropped, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The time \( t \) taken for the stone to hit the ground is \( 10 \) seconds.
- The acceleration due to gravity \( g \) is approximately \( 9.8 \, \text{m/s}^2 \).

2. **Use the Formula for Distance**:
- When an object is dropped from rest, the distance \( h \) it falls can be calculated using the formula:
\[ h = \frac{1}{2} g t^2 \]

3. **Substitute the Values into the Formula**:
- Substitute \( g = 9.8 \, \text{m/s}^2 \) and \( t = 10 \, \text{s} \) into the formula:
\[ h = \frac{1}{2} \times 9.8 \times (10)^2 \]

4. **Calculate \( t^2 \)**:
- Calculate \( (10)^2 \):
\[ (10)^2 = 100 \]

5. **Calculate the Height**:
- Now substitute \( t^2 \) back into the equation:
\[ h = \frac{1}{2} \times 9.8 \times 100 \]
- Simplifying this gives:
\[ h = \frac{980}{2} = 490 \, \text{meters} \]

6. **Conclusion**:
- The height of the tower is \( 490 \, \text{meters} \).

### Final Answer:
The height of the tower is **490 meters**.

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