A batter hits a pitched ball when the centre of the ball is 1.22 m above the ground. The ball leaves the bat at an angle of `45^(@)` with the ground. With that launch, the ball should have a horizontal range (returning to the launch level) of 107 m. (a) Does the ball clear a 7.32-m-high fence that is 9.75 m horizontally from the launch point? (b) At the fence, what is the distance between the fence top and the ball center?

Explanation

To solve the problem step by step, we will analyze the projectile motion of the ball and determine whether it clears the fence and the distance between the top of the fence and the center of the ball.

### Step 1: Determine the Initial Velocity
We know that the horizontal range \( R \) of a projectile launched at an angle \( \theta \) is given by the formula:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]
Given:
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