To determine how far the ball travels when it hits the ground, we need to solve the equation for \( h(x) = 0 \):
\[ 0 = -\frac{1}{25}x(x - 45) \]
This equation will be zero when either \( x = 0 \) or \( x - 45 = 0 \).
- Finding the roots:
- From \( x = 0 \), the ball is at the initial position.
- From \( x - 45 = 0 \), we find \( x = 45 \).
Thus, the ball will hit the ground after it has traveled 45 yards.
- Determining how far it needs to roll to reach the hole: The hole is 55 yards away, and the ball travels 45 yards to the ground, leaving:
\[ 55 - 45 = 10 \text{ yards} \]
Therefore, the ball will need to roll an additional 10 yards to reach the hole.
So, 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.