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To determine how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \). The equation given is:
\[
0 = -\frac{1}{30} x(x - 61)
\]
To find the points where the ball hits the ground, we can set the equation inside the parentheses to zero:
\[
-\frac{1}{30} x(x - 61) = 0
\]
Now, we can solve for \( x \):
1. The product \( x(x - 61) = 0 \) gives us two solutions:
- \( x = 0 \)
- \( x - 61 = 0 \) which leads to \( x = 61 \)
Thus, the points at which the height \( h(x) = 0 \) are \( x = 0 \) yards (when the ball is just kicked) and \( x = 61 \) yards (when the ball hits the ground).
Therefore, the ball will have traveled **61 yards** before hitting the ground.