A projectile is thrown upward so that its distance above the ground after t seconds is given by thefunctionh(t)=-16t2+576t.

Question

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 576t. After how many seconds does the projectile take to reach its maximum height?

Answer 1

For the parabola:

h(t) = -at² + bt, the maximum occurs at -b/2a

For h(t) = -16t² + 576t that is -576/(-2)(-16), or -576/32, or 18.

The projectile is at its highest point at 18 seconds.