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

Question

, 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)

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:

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

First, we can simplify this equation. We can multiply both sides by -30 to eliminate the fraction:

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

Now, we can set the equation to zero by factoring:

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

From this equation, we set each factor to zero:

1. \( x = 0 \)
2. \( x - 61 = 0 \) which gives \( x = 61 \)

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

The value \( x = 0 \) corresponds to the starting point of the kick. The value \( x = 61 \) represents the horizontal distance traveled when the ball hits the ground.

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