To determine how far the ball travels when it hits the ground, we need to solve the equation given by the height function \( h(x) = -125x(x - 45) \). We set \( h(x) = 0 \) to find the values of \( x \) when the ball hits the ground:
\[ 0 = -125x(x - 45) \]
This equation can be factored into two parts:
- \( -125x = 0 \) which gives \( x = 0 \)
- \( x - 45 = 0 \) which gives \( x = 45 \)
The two solutions to the equation are \( x = 0 \) and \( x = 45 \). This means the ball hits the ground when it has traveled 45 yards.
Now, if the hole is located at 55 yards from the starting point (as inferred from the context), we can find how far the ball needs to roll after it hits the ground:
\[ \text{Distance to the hole} - \text{Distance traveled} = 55 - 45 = 10 \text{ yards} \]
So, the ball will hit the ground after it has traveled 45 yards, and it will need to roll an additional 10 yards to reach the hole.
Based on the options provided, 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.