To determine how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \):
\[ 0 = -125x(x - 45) \]
This equation will equal zero when either factor is zero:
- \( -125x = 0 \) which gives \( x = 0 \)
- \( x - 45 = 0 \) which gives \( x = 45 \)
The solutions to the equation \( h(x) = 0 \) are \( x = 0 \) and \( x = 45 \). This means the ball will hit the ground after it has traveled 45 yards.
Now, since the hole is 55 yards away, we determine how far the ball will need to roll after it hits the ground:
\[ \text{Distance to the hole} = 55 \text{ yards} \] \[ \text{Distance traveled by ball} = 45 \text{ yards} \] \[ \text{Distance to roll} = 55 - 45 = 10 \text{ yards} \]
Thus, the 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.