To determine where the ball will hit the ground, we need to solve the equation \( h(x) = 0 \):
\[ 0 = -125x(x - 45) \]
Setting each factor equal to zero gives us:
- \( -125x = 0 \) → \( x = 0 \)
- \( x - 45 = 0 \) → \( x = 45 \)
The two solutions indicate that the ball will be at ground level (height \( h(x) = 0 \)) when it has traveled \( 0 \) yards (when it is initially hit) and \( 45 \) yards (when it hits the ground).
Since the hole is \( 55 \) yards away and the ball hits the ground at \( 45 \) yards, we calculate how far the ball will need to roll to reach the hole:
\[ \text{Distance to roll} = \text{Distance to hole} - \text{Distance traveled before hitting ground} = 55 \text{ yards} - 45 \text{ yards} = 10 \text{ yards} \]
Thus, the ball will hit the ground after it has traveled \( 45 \) yards and 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.