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 both particles and find the time at which they meet after the first particle is projected. Let's denote the following:

- \( u \): initial velocity of both particles
- \( g \): acceleration due to gravity
- \( t \): time difference between the projections of the two particles

### Step 1: Analyze the motion of the first particle

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