To begin a football game, a kicker has to kick off. The football follows the path h(x)=−1/30x(x−61), where h(x) is the height of the football and x is the horizontal distance it has traveled in yards. Solve the equation to determine how far the ball will have traveled when it hits the ground.

To determine how far the ball will have traveled when it hits the ground, we need to solve the equation:

\[ 0 = -\frac{1}{30}x(x - 61) \]

We can solve this equation by setting the expression equal to zero:

\[ -\frac{1}{30}x(x - 61) = 0 \]

Since the product of two factors is equal to zero, we can set each factor to zero:

1. \( x = 0 \)

or

2. \( x - 61 = 0 \) → \( x = 61 \)

The two solutions are \( x = 0 \) and \( x = 61 \). The first solution, \( x = 0 \), corresponds to the ball being kicked (at the start), while the second solution, \( x = 61 \), corresponds to the ball hitting the ground.

Thus, the ball will have traveled 61 yards before hitting the ground.