I HAVE NO CLUE
11. A punter kicks a football. Its height, h, in meters, t seconds after the kick is given by the equation h= –4.9t² + 18.24t + 0.8. The height of an approaching blocker's hands is modeled by the equation h= –1.43t + 4.26, using the same time. Can the blocker knock down the punt? If so, at what point will it happen?

Question

I HAVE NO CLUE
11. A punter kicks a football. Its height, h, in meters, t seconds after the kick is given by the equation h= –4.9t² + 18.24t + 0.8. The height of an approaching blocker's hands is modeled by the equation h= –1.43t + 4.26, using the same time. Can the blocker knock down the punt? If so, at what point will it happen?

mrnood · Answer

This is a fairly contrived question - but the key point is that if the blocker's hand can touch the  ball then the height of the hand must be the same as the height of the ball

so
–4.9t² + 18.24t + 0.8=–1.43t + 4.26

rearrange this into a simple quadratic.

If it has real roots (solutions for t) then the blocker can touch the  ball.

mrnood · Answer

( the reason it seems contrived to me? at t=0 the blockers hand is 4.26m high. That is 14ft high)