Let's look at another one of Homer's rocket launches. It was launched from ground level with an initial velocity of 208 feet per second. Its distance in feet from the ground after t seconds is given by S (t) = - 16t2 + 208t. What is the maximum altitude (height) the rocket will attain during its flight? (Think about where the maximum value of a parabola occurs.)

Smax = 676 ft

the maximum altitude (height) the rocket will attain during its flight is 676 ft

Step-by-step explanation:

Given;

The height function S (t) of the rocket as;

S (t) = - 16t2 + 208t

The maximum altitude Smax, will occur at dS/dt = 0

differentiating S (t);

dS/dt = - 32t + 208 = 0

-32t + 208 = 0

32t = 208

t = 208/32

t = 6.5 seconds.

The maximum altitude Smax is;

Substituting t = 6.5 s

Smax = - 16 (6.5) ^2 + 208 (6.5)

Smax = 676 ft

the maximum altitude (height) the rocket will attain during its flight is 676 ft