Two bodies are thrown up at angles of `45^(@)` and `60^(@)` respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocity with which these are thrown is `sqrt(x/2)`. Find the value of x.

Explanation

To solve the problem, we need to find the value of \( x \) given that two bodies are thrown at angles of \( 45^\circ \) and \( 60^\circ \) respectively, and they attain the same vertical height. The ratio of their initial velocities is given as \( \sqrt{\frac{x}{2}} \).

### Step-by-step Solution:

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