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 have traveled when it hits the ground, we need to solve the equation:

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

This equation is equal to zero when either of the factors is zero:

1. \(-\frac{1}{30} = 0\) is not true, so we focus on the two factors:

2. The first factor (which we can ignore since it does not equal zero) is:
\[
x = 0
\]

3. The second factor is:
\[
x - 61 = 0 \implies x = 61
\]

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

The ball will have traveled \(61\) yards before hitting the ground (since \(x = 0\) represents the starting point).

So, the final answer is:

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