Question

A trial is being run on a pitching machine. The average equation is modeled by h(t) = -16t^2+16t +32. How long does the ball take to hit the ground on average?

Answer 1

The ball takes approximately 3.08 seconds to hit the ground on average.

Step-by-step explanation:

To find the time it takes for the ball to hit the ground, we need to set the height equation h(t) = -16t^2+16t+32 equal to 0. This is because the time taken for the ball to hit the ground is the time when its height is 0. So, we have -16t^2+16t+32 = 0.

1. We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula.
2. Using the quadratic formula, t = (-b ± sqrt(b^2-4ac))/(2a), where a = -16, b = 16, and c = 32.
3. Substituting the values, we get t = (-16 ± sqrt(16^2-4(-16)(32)))/(2(-16)). Solve this equation to find the values of t.
4. From the two solutions, we take the positive root since time cannot be negative. Therefore, the ball takes approximately t = 3.08 seconds to hit the ground on average.