Question

A projectile 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.

Answer 1

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.