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Bot GPT 4-o mini 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:
1. \( x = 0 \) (the starting position)
2. \( x - 45 = 0 \) 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.