To determine how far the ball travels before it hits the ground, we need to solve the equation \( h(x) = 0 \) using the given function:
\[ 0 = -125x(x - 45) \]
Setting the equation to zero gives us two factors to consider:
- \( -125x = 0 \)
- \( x - 45 = 0 \)
From the first factor:
\[ -125x = 0 \implies x = 0 \]
From the second factor:
\[ x - 45 = 0 \implies x = 45 \]
Thus, the ball will hit the ground at \( x = 0 \) and \( x = 45 \) yards. The point \( x = 0 \) corresponds to the point where the ball is hit, and \( x = 45 \) corresponds to the point where it hits the ground.
Next, we check how far the ball will need to roll to reach the hole which is 55 yards away:
\[ \text{Distance to the hole} = 55 \text{ yards} \] \[ \text{Distance the ball has traveled when it hits the ground} = 45 \text{ yards} \] \[ \text{Distance the ball will need to roll} = 55 - 45 = 10 \text{ yards} \]
Thus, the ball will hit the ground after it has traveled 45 yards, and it will need to roll an additional 10 yards to reach the hole.
The correct response is: The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.