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)

Question

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 set the equation equal to zero:

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

For the product to equal zero, either \(x = 0\) or \(x - 61 = 0\).

1. The first solution is: \[ x = 0 \]

2. The second solution is: \[ x - 61 = 0 \implies x = 61 \]

Thus, the two values of \(x\) that satisfy the equation are \(x = 0\) and \(x = 61\).

The value \(x = 0\) corresponds to the moment the ball is kicked (the kickoff point), while \(x = 61\) yards is when the ball hits the ground.

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