Determine how much time it takes a rocket to reach its full height.

Question

The path of a small rocket is given by the equation h(t)=-16^2+128t where h is height in feet and t is time in seconds. Determine how much time it takes a rocket to reach its full height.

Answer 1

Two possible ways to get the solution.

If you have taken calculus, you know that the maximum occurs when the derivative is zero.

h(t)=-16t²+128t

h'(t)=-32t+128=0 so t=4s.

If you didn't take calculus, you can note that the trajectory (path of the object) is a parabola and determine that the vertex will give you the maximum. The steps involve completing the square:

h(t)=-16t²+128=-16(t²-8t)=-16(t² -8t +16-16)=-16[(t-4)²-16]

Thus the maximum occurs at t=4s and the maximum height is -16(-16)=256m.