Aprojectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t^2 + 576t. after how many seconds does the projectile take to reach its maximum height? show your work for full credit.

The time required for the maximum height to be attained is calculated by differentiating the given equation and equating the derivative to zero. 
                                    h(t) = -16t² + 576t
                            dh(t) / dt = 0 = (-16)(2)t + 576
The value of t from the equation is 18. Thus, after 18 seconds the projectile reaches its maximum height. 
                                   

Answer body lying face up ;