Question

A punter kicks a football. Its height h, in yard, t seconds after the kick is given by the equation h(t)=-4.9t^2+18.24t+0.8. The height of an approaching blocker's hand is modeled by the equation h(t)=-1.43t+4.26, using the same time. Can the blocker knock down the punt (do they intersect)? If so, at what point will that happen (the point of intersection)?

Answer 1

Part 1

`-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0`

Therefore, the blocker can knock down the punt.

Part 2

Using the quadratic formula,

`t=(-19.67 \pm √(319.0929))/(2(-4.9))\\\\t \approx 0.18437, 3.82992`

Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is
`(0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}`.