To find out how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \):
\[ 0 = -\frac{1}{25} x(x - 45) \]
This equation can be set to zero for values of \( x \):
\[ -\frac{1}{25} x(x - 45) = 0 \]
The product \( x(x - 45) \) must equal zero. This gives us:
- \( x = 0 \)
- \( x - 45 = 0 \) which simplifies to \( x = 45 \)
This means the ball hits the ground after it has traveled either \( 0 \) yards (the starting point) or \( 45 \) yards. Therefore, the ball will hit the ground after it has traveled 45 yards.
Since the hole is 55 yards away, we now determine how far the ball will need to roll to reach the hole:
\[ \text{Distance to hole} = 55 \text{ yards} - 45 \text{ yards} = 10 \text{ yards} \]
Thus, the ball will need to roll an additional 10 yards to reach the hole.
Putting this together, 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.