A particle is dropped from the top of a tower. If it falls half of the height of the tower in its last second of journey, find the time of journey.

Explanation

To solve the problem of a particle dropped from the top of a tower, where it falls half of the height of the tower in its last second of journey, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A particle is dropped from a height \( H \).
- It falls freely under gravity, with an initial velocity \( u = 0 \).
- We need to find the total time of the journey \( n \) seconds, given that the distance fallen in the last second is \( \frac{H}{2} \).
...