A particle is projected vertically upwards and t second after another particle is projected upwards with the same initial velocity. Prove that the particles will meet after a lapse of `((t)/(2)+(u)/(g))` time from the instant of projection of the first particle.

Explanation

To solve the problem, we need to analyze the motion of two particles projected vertically upwards with the same initial velocity \( u \). The first particle is projected at \( t = 0 \) and the second particle is projected \( t \) seconds later.

### Step-by-Step Solution:

1. **Equations of Motion for Particle 1**:
The first particle is projected at \( t = 0 \). The equations of motion for this particle can be written as:
- Velocity:
\[
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