The maximum height attain by a projectile is increased by ` 10%` by increasing its speed of projection, without changing the angle of projection. What will the percentage increase in the horizontal range.

Explanation

To solve the problem, we need to find the percentage increase in the horizontal range of a projectile when its maximum height is increased by 10% due to an increase in the speed of projection, while keeping the angle of projection constant.

### Step-by-Step Solution:

1. **Understanding the Maximum Height Formula**:
The maximum height \( H \) attained by a projectile is given by the formula:
\[
H = \frac{U^2 \sin^2 \theta}{2g}
...