To determine how far the ball will have traveled when it hits the ground, we need to solve the equation given by the height function \( h(x) \):
\[ 0 = -\frac{1}{25} x (x - 45) \]
This equation can be solved by setting each factor to zero:
- \( -\frac{1}{25} x = 0 \) leads to \( x = 0 \) (initial position)
- \( x - 45 = 0 \) leads to \( x = 45 \)
Now we interpret these roots in the context of the problem:
- \( x = 0 \) represents the starting point when the golf ball is hit.
- \( x = 45 \) indicates where the ball hits the ground.
Thus, the ball will hit the ground after it has traveled 45 yards.
Next, we need to find out how far it will need to roll to reach the hole, which is 55 yards away:
\[ \text{Distance needed to roll} = 55 \text{ yards (to the hole)} - 45 \text{ yards (distance traveled)} = 10 \text{ yards} \]
So we can conclude:
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.
The correct statement 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.