A particle is projected vertically upwards. Prove that it will be at three-fourth of its greatest height at times which are in the ratio `1: 3`.

Explanation

To solve the problem of a particle projected vertically upwards and to prove that it will be at three-fourths of its greatest height at times which are in the ratio 1:3, we can follow these steps:

### Step 1: Determine the maximum height (H)
When a particle is projected vertically upwards with an initial velocity \( u \), the maximum height \( H \) it reaches can be calculated using the formula:
\[ H = \frac{u^2}{2g} \]
where \( g \) is the acceleration due to gravity.
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