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.

s(2) = 38 meters

I don't know if you are a calculus student, but since calculus is the easiest way to solve this, that's what I used.  The position equation is

and the velocity function, the first derivative, is

From Physics, you should know that the velocity of an object is 0 at its highest point.  That means that if we sub in a 0 for the velocity and solve for t, we find the time at which the object is at its highest point.  That is:

and

By the Zero Product Property,

-12 definitely does not equal 0, so that means that

t - 2 = 0 and

t = 2 seconds.

So at 2 seconds, the object is at its highest point.  Go back to the position function now and sub in a 2 for t to find the height of the object at 2 seconds.

so

s(2) = 38 meters

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have