To determine how far the football will have traveled when it hits the ground, we need to set the height \( h(x) \) equal to zero and solve for \( x \). The function given is:
\[ h(x) = -\frac{1}{30}x(x-61) \]
Setting it equal to zero:
\[ 0 = -\frac{1}{30}x(x-61) \]
To solve this equation, we can multiply both sides by -30 (to eliminate the fraction):
\[ 0 = x(x-61) \]
Now we can factor the equation:
\[ x(x-61) = 0 \]
Setting each factor equal to zero gives us:
- \( x = 0 \)
- \( x - 61 = 0 \) ⇒ \( x = 61 \)
Thus, the solutions are \( x = 0 \) and \( x = 61 \).
In the context of the football's path, \( x = 0 \) represents the point where the ball is kicked from, and \( x = 61 \) represents the point where the ball hits the ground.
Therefore, the ball will have traveled 61 yards when it hits the ground.