To determine how far the ball will have traveled when it hits the ground, we need to solve the equation:
\[ 0 = -\frac{1}{25}x(x - 45) \]
This equation can be factored as:
\[ 0 = -\frac{1}{25}x(x - 45) \]
Setting the product equal to zero gives us two solutions:
- \( x = 0 \) (the starting position)
- \( x - 45 = 0 \) which leads to \( x = 45 \)
Thus, the ball will reach the ground after traveling 45 yards.
Now, since the hole is 55 yards away, we can determine how far the ball needs to roll after hitting the ground:
\[ \text{Distance to hole} = 55 \text{ yards} \] \[ \text{Distance traveled before hitting ground} = 45 \text{ yards} \] \[ \text{Rolling distance} = 55 - 45 = 10 \text{ yards} \]
Therefore, 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.