Question

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.

0=−1/30x(x−61)

(1 point)
The ball will have traveled yards before hitting the ground.

Answer 1

To determine how far the ball will travel before hitting the ground, we need to solve the equation:

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

We can start by multiplying both sides by \(-30\) to eliminate the fraction:

\[
0 = x(x - 61)
\]

Now we set the expression equal to zero:

\[
x(x - 61) = 0
\]

This product will equal zero when either of the factors is equal to zero. Therefore, we can set each factor to zero:

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

The solutions to the equation are \(x = 0\) and \(x = 61\).

The \(x = 0\) solution corresponds to the initial position of the ball at the kickoff, while \(x = 61\) corresponds to the position where the ball hits the ground.

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