Question

To begin a football game, a kicker has to kick off. The football follows the path h(x)=− 1/30 x(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=− 1/30 x(x−61)

(1 point)
The ball will have traveled
yards before hitting the ground.
Remaining Attempts : 3
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Answer 1

To determine how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \), which means setting the height function to zero:

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

To solve this, we can first simplify the equation. Since the function is multiplied by \(-\frac{1}{30}\), we can multiply both sides by \(-30\) (which will not change the equality) to eliminate the fraction:

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

Next, we can factor this equation:

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

Setting each factor equal to zero gives us:

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

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

The value \( x = 0 \) represents the point where the football is kicked (the starting point). The value \( x = 61 \) represents the horizontal distance traveled when the football hits the ground.

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