Question

A punter kicks a football. Its height in meters is given by the function, h(t) = -4.9t2 + 18.42t +0.8, where h represents the height (meters) and t represents the

time, in seconds. The height of an approaching blocker's hands can be modeled by the equation, h(t) = -2.21t+ 7.45 using the same time. Can the blocker knock
down the punt? If so, at what time does this happen?

Answer 1

approximately 0.331 seconds.

Explanation:

In order to determine if the blocker can knock down the punt, we need to find the time at which the heights of the football and the blocker's hands are equal. By setting the two height functions equal to each other and solving for t, we get a quadratic equation: -4.9t^2 + 20.63t - 6.65 = 0. We can use the quadratic formula to solve for t: t = (-b ± √(b^2 - 4ac)) / (2a). If we plug in the values from our quadratic equation, we get two possible solutions for t: t ≈ 0.331 seconds and t ≈ -3.244 seconds. Since time cannot be negative in this context, we can disregard the second solution, and conclude that the blocker can potentially knock down the punt at