A ball drops from a celling of a room and after rebounding twice from the floor reaches a height equal to half that of the ceiling. If th coefficient of restitution is `(1/2)^(1//x)`. Find the value of x.

Explanation

To solve the problem, we need to find the value of \( x \) given that a ball dropped from the ceiling rebounds twice and reaches a height equal to half that of the ceiling. The coefficient of restitution is given as \( \left( \frac{1}{2} \right)^{\frac{1}{x}} \).

### Step-by-Step Solution:

1. **Define Variables**:
Let \( h \) be the height of the ceiling. The ball is dropped from this height.

2. **Calculate Initial Velocity**:
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