A model rocket is launched from the top of a building. The height (in meters) of the rocket above the ground is given by h( t) = -16t²+ 96t + 14, where t is the time (in seconds) since the rocket was launched. What is the rocket’s maximum height and when does this occur.

Question

A model rocket is launched from the top of a building. The height (in meters) of the rocket above the ground is given by h( t)  = -16t²+ 96t + 14, where t is the time (in seconds) since the rocket was launched. What is the rocket’s maximum height and when does this occur.

R_scott · Answer

the max is on the axis of symmetry of the parabola tmax = -b / 2a = -96 / (2 * -16) = 3 s plug the 3 into h(t) to find the max height