To determine how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \):
\[ h(x) = -125x(x - 45) \]
Setting \( h(x) = 0 \):
\[ -125x(x - 45) = 0 \]
This equation can be factored into two parts:
- \( -125x = 0 \) which gives \( x = 0 \)
- \( x - 45 = 0 \) which gives \( x = 45 \)
Thus, the solutions to the equation are \( x = 0 \) and \( x = 45 \). This means the ball will hit the ground after traveling \( 45 \) yards.
To determine how far the ball rolls to reach the hole, which is \( 55 \) yards away, we subtract the distance it traveled before hitting the ground from the total distance to the hole:
\[ \text{Distance to the hole} - \text{Distance traveled} = 55 \text{ yards} - 45 \text{ yards} = 10 \text{ yards} \]
Therefore:
- 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.
None of the provided response options match this conclusion exactly, as the ball travels \( 45 \) yards before hitting the ground, not \( 25 \) or \( 10 \) yards as listed in the options.
The correct answer 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.