Question

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t2 + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.

Answer 1

If h(t) represents distance, and velocity is \(v(t)=\cfrac{dh(t)}{dt}\) and we know that at the maximum, \(v(t)=0\). So, take the derivative of h(t), set it equal to zero and solve for t.

You can also graph h(t) and find out when it reaches its maximum. You know that this is a parabola because of the term t^2, so you can use this as well. If you find out where h(t)=0, then the maximum will be half-way between these two times. You know this because parabolas are symmetric about its maximum.


If you don't know calculus, then you will need to use the second approach.