To begin a football game, aa kicker has to kick off. The football follows the path h (x) = -1/30x (x - 61), where h 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 to travel when it hits the ground.

Question

0 = -1/30x (x - 61)

The ball will have traveled ____ yards before hitting the ground.

Answer 1

To find the distance \( x \) the football travels before hitting the ground, we need to solve the equation

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

First, we can factor this equation. Setting the equation equal to zero, we have:

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

This equation equals zero if either \(-\frac{1}{30} = 0\) (which is not true) or if the product \(x(x - 61) = 0\).

From the product \(x(x - 61) = 0\), we can set each factor to zero:

1. \(x = 0\)
2. \(x - 61 = 0 \Rightarrow x = 61\)

Thus, the possible values of \(x\) are \(0\) and \(61\).

The ball will hit the ground when \(x = 61\) since \(x = 0\) represents the starting point of the kick off.

Therefore, the ball will have traveled

\[ \boxed{61} \]

yards before hitting the ground.