A stone is projected at an angle of `30^(@)` with the vertical. If the horizontal component of its velocity is `9.8m//s` , calculate the maximum height attained by the stone and its horizontal range .

Explanation

To solve the problem of a stone projected at an angle of \(30^\circ\) with the vertical, we will calculate the maximum height attained by the stone and its horizontal range. Given that the horizontal component of its velocity is \(9.8 \, \text{m/s}\), we can follow these steps:

### Step 1: Determine the Initial Velocity
The horizontal component of the velocity (\(V_x\)) is given as \(9.8 \, \text{m/s}\). Since the angle of projection with the vertical is \(30^\circ\), the angle with the horizontal is \(60^\circ\) (because \(90^\circ - 30^\circ = 60^\circ\)).

Using the relationship for horizontal velocity:
\[
V_x = V \cos(60^\circ)
...